The "Vegas Enclave" (or the United States of America under House) basically has many things that were good and bad about America rolled into one package. Manifest Destiny, inclusion of diverse elements, capitalism, jingoism, and McCarthy-style paranoia about Communism, except this time, it's been changed so that they're paranoid against the Brotherhood of Steel.
Robert Edwin House is at the center of this new Enclave, since he is the new Enclave President, and he sees the Brotherhood of Steel as a relic of a bygone age of darkness when America was at its nadir. He sees them as relics of the Dark Ages, stifling progress while cosplaying as knights, while House sees himself as an enlightened man practicing the same enlightenment values the Founding Fathers preached, reviving America and leading mankind to a new future where they will eventually explore the stars.
While House has nothing against religion (indeed, he even makes compromises with churches that survived the apocalypse, especially Joshua Graham's Mormon Church) House does have a bone to pick with what he sees as superstitions that make no sense and have no value to the outside world, the primary example of that being the Codex of the Brotherhood of Steel, its ideas, its beliefs, and the way it preaches to the Brotherhood that they must keep technology to themselves while leaving the wastelanders to their fate. House sees that ideology as a complete waste.
The way House sees it, technology must be shared, and the wastelanders have to be uplifted. He manages the Vegas Enclave the exact same way he managed New Vegas. He uplifts tribes and communities who accept his rule, eradicates those who resist, and those tribals and primitives who are accepted into the system have the "tribal" taken out of them and forcibly civilized, the same way America tried to eradicate Indian culture by sending Indian boys to boarding schools to make them good little WASP boys in Indian skin. Once uplifted, these newly-civilized folk are made to work in factories, farms, and the service sector, or made into soldiers for the cause. Following a similar pattern to Caesar's Legion, House has large tribes and families either assimilated or broken up, has tattoos burned off, and forces mixed-race marriages to eradicate any previous loyalties, and with Caesar and the Legion helping him in that regard, House carries this pattern out, day by day, as they conquer lesser tribes on their march eastward.
Like Emperor Justinian before him, House seeks to bring the ideas of America back to the land that gave birth to it, just as Justinian sought to return the Roman Empire to its splendor by reconquering the lands that gave birth to the Empire to begin with. And like the Americans of the past, the Vegas Enclave has this "Manifest Destiny" idea that everything from sea to shining sea belongs to them, and they long for the day when they can take Washington DC from the Brotherhood of Steel and restore the American capital to glory. Some of the Enclave soldiers serving in House's armies were former East Coast Enclave troops under President John Henry Eden, and they've been looking for a chance to get some payback against the East Coast Brotherhood that drove them out of their nation's capital.
America's diversity is also part of the Vegas Enclave's makeup. The Vegas Enclave military is a hodge-podge of ex-NCR soldiers and Rangers, Legion troops, Enclave power-armored soldiers, and Securitrons, all under a single command structure. Each part of the Vegas Enclave military has its own operating procedures, even though by the end of the day, the Enclave soldiers sit at the top, commanding both California and Legion troops underneath their heel. The best of the latter two are admitted into the Enclave and given power armor, though some choose to stay within their respective groups due to nostalgia.
From the NCR Rangers, the Vegas Enclave forces learn survival skills out in the wild and accuracy with high-caliber ballistic weapons. From the Legion soldiers, the Vegas Enclave forces took their robust training regimen, their practice of taking healthy young boys to be trained as soldiers, and their proficiency with melee weapons. Other groups such as the Boomers and religious groups like the New Canaanites also contributed, with the Boomers teaching the Vegas Enclave their extensive knowledge on using explosives and bomber aircraft, while New Canaanites and other religious fighters serve as battle chaplains on the front lines, preaching the Good News while wielding weapons like .45 automatic pistols. And of course, the Enclave soldiers themselves teach power armor training and the use of energy weapons to new recruits.
However, the bad parts of each army also filtered into the Vegas Enclave and its military. NCR and Enclave soldiers have a propensity for shooting criminals and fugitives on sight, something which didn't go away when they were united under the umbrella of House's Enclave forces, and the Legion's propensity for cruelty also seeped in, with Vegas Enclave forces taking up their practices of torturing, beheading, crucifying, and enslaving those who did not bend the knee to them. Seeing power-armored Enclave troopers burning down whole towns and crucifying important dissidents with the help of Legion Centurions while NCR Veteran Rangers form firing squads to execute the rabble amongst the rebels is an increasingly common sight.
Like pre-war America, House's Enclave has a very "with us or against us" vibe going on. The constant propaganda that the civilians are bombarded with about life under Brotherhood control goes from realistic (people are constantly robbed of technological gadgets the Brotherhood sees fit to take from them) to exaggerated. (The Brotherhood butchers entire communities for having forbidden knowledge that they want to keep to themselves.) However, there are certain inklings of truth even in their propaganda broadcasts, as many of these tales are usually eyewitness accounts from people who fled Brotherhood territory for Enclave turf. Insults that the Legion once used against the NCR are used by the Enclave populace against the Brotherhood of Steel and its supporters, with the word "profligate" used often, as House sees the Brotherhood as profligates for wasting their technological resources on a petty preservation of power instead of helping to uplift mankind back from the Dark Ages.
Many intelligent Super Mutants, ghouls, and synths flee to Enclave territory, fearing the genocidal wrath of the Brotherhood, and the Vegas Enclave takes them all in, with House using them as propagandizers to rally support against the Brotherhood. Unlike past Enclave leaders, House has no problems with ghouls or Super Mutants, and he himself resides in a synth body, so he has no problem tolerating them so long as they follow his laws.
Local citizens are rewarded for turning in Brotherhood spies, while anyone accused of working with the Brotherhood of Steel are jailed at best, and executed at worst, with those who carry out Brotherhood operations on Enclave soil usually getting crucified, although some do end up getting enslaved if they were physically fit or desirable in the eyes of some buyers. Propaganda posters denouncing the Brotherhood are all over Enclave towns and cities, while major plays, TV shows, movies, and radio dramas based on the horror stories about Brotherhood rule have become some of the most popular media in Enclave territory, with some ghouls, synths, and super mutants even becoming rich celebrities for their acting roles in such works.
Speaking of celebrities making a killing, capitalism is in full force in House's America. Brahmin barons, landowners, factory owners, and other business leaders have many privileges in society, down to the point where they became a sort of nobility in the new Enclave. However, there is a limited form of welfare encouraged by groups like the New Canaanites and the Followers of the Apocalypse, and many people live content lives due to the fact that the government provides for education, medicine, technology, and new farming methods have allowed them to produce food at an astonishing rate. However, charity outside of religious leanings is still mostly frowned upon, and aside from the continued demonization of Communism, children are taught that America's capitalist values were always correct. The kids in schools are made to learn about how Mr. House built a corporate empire through his ingenuity and hard work, and they are taught to follow that example. House encourages those with bright young minds and potential to work for him in exchange for wealth, recognition, and fame.
The Brotherhood of Steel, on the other hand, has its own propaganda and its own views on the world. They see themselves as fighting the same war they were fighting all the way back in Fallout 2. They see themselves as the heirs of civilization, protecting humanity from making the same mistakes all over again, and to them, House is repeating the mistakes of the past. They see him as a dangerous renegade, giving away technology like power armor and energy weapons to savages, and upon learning that he's part-synth, to them, he's an inhuman abomination who should have died long ago.
Arthur Maxson's Brotherhood recalls the glory days of defeating the Master and his Super Mutant Army, of their victories against the Enclave in California and Washington DC, and their triumph against the Institute in the Boston Commonwealth. Upon learning that synths, Super Mutants, ghouls, and members of the East Coast Enclave have joined with House, the Brotherhood began seeing House's Enclave as the amalgamation of all the enemies they fought in the past, a representation of everything wrong in the wasteland, and they acted as if the Vegas Enclave was some sort of "final enemy" that has all their former enemies in one convenient package for them to blow up.
The Brotherhood, having been victorious in their previous battles thus far, continued to be set in their cultish ways. Arthur Maxson has his men teach their students the same lessons that the Brotherhood Codex taught initiates for years: that savages in the wastelands should not be allowed to have their hands on such dangerous technology. They see House giving away gifts like securitrons, power armors, and energy weapons to the profligates of the NCR and the savages of the Legion, and they see it as if House was giving away nuclear weapons to cavemen. They see more and more people wearing Enclave armors with pride, and many Brotherhood Paladins grow angry, remembering the days when Enclave soldiers gunned down wastelanders without a care in the world. They see House expanding his power and eradicating entire communities who don't bow down to him, and they take it as proof that House isn't out to revive America, but to just increase his own power at the expense of others.
After learning of the California Brotherhood's destruction at the hands of House's forces, Arthur Maxson's Brotherhood had their elite guard, known as the "Avengers of Steel", dress up in black and red armor to commemorate the dead, with black as the traditional color for mourning the dead, and red, to symbolize the blood of their California brothers whom they see as martyrs.
The people of the Brotherhood of Steel continued to mock the idea that House's "United States" is a revival of America, insisting instead that House is acting like every self-aggrandizing warlord in history, and that he's just using the symbols of old America to support his drive for power. To a certain extent, they are correct, as House's America is more authoritarian than America was during its golden years, but not during its pre-war years. Upon learning that House took over Caesar's Legion, Arthur Maxson once joked that House would be more fit to be called "Kaiser" than "President", which led to the Brotherhood Paladins calling the Enclave President "Kaiser House", an obvious reference to the autocratic Kaiser Wilhelm II and his aggressive expansion policy before World War 1.
The Brotherhood sees itself as the true inheritors of post-apocalyptic America, tracing their ancestry back to members of the United States Army who deserted upon finding out about the evils of pre-war America, and to them, fighting House is a war against the same evil system that Roger Maxson rebelled against. The Brotherhood continued to teach its students about the flaws of pre-war America, and in Arthur Maxson's mind, trying to revive the horribly flawed nation that ruled the land before it got nuked shows that House and his ilk have learned nothing from the nuclear war.
The fact that House continued to give away freely things that Arthur Maxson saw as dangerous technology made House an easy target for propaganda in Brotherhood circles, where he is portrayed as a madman who didn't care about the delicate balance of the wasteland. They compare House's brutal and imperialistic approach to outside tribes and communities to how tribes and communities in Brotherhood territory are left alone to manage their own affairs, and they take that as proof positive that they are the true defenders of democracy and freedom, while House's Enclave is just a mockery towards democracy and the American way that they say they serve.
The Brotherhood's actual record towards the communities under its umbrella, however, are mixed. While for the most part, they have eradicated groups of Super Mutants and ghouls that posed a threat, the Brotherhood also has a record of forcibly confiscating technology from places without the locals' consent. They had no problems taking bits and pieces of tech from Rivet City, Diamond City, and any other town that may have technology they deem fit to keep to themselves. At one point, they came across a town that used power armor and laser weapons to keep a bunch of Deathclaws at bay, but since the Deathclaws never threatened the Brotherhood, the Brotherhood came in and took the town's laser weapons and power armors for their war effort against the Enclave, leaving the town to fend for itself with low-caliber guns to use against the Deathclaws, which led to the town getting annihilated. Other towns and cities that resisted having the Brotherhood confiscating their tech would typically get sacked by the Brotherhood forces, with any Brotherhood members who objected to this sort of behavior getting expelled from the group.
At the same time, some communities who are attacked by human raiders get almost no help from the Brotherhood, since they're not being attacked by Super Mutants, ghouls, or synths, and so long as the raiders steered clear of any Brotherhood patrols and didn't hoard tech to themselves, they were left alone, forcing these towns and cities to arm themselves with ballistic weapons to fend off the raiders. Some paladins do occasionally help out against raiders, but usually because they felt like it, not because they were ordered to. The official standing order from Elder Maxson is to focus on mutant and synth threats, while preparing for the big war against the Enclave, so going off adventuring and killing raiders on their own was discouraged among the Paladins, as it would damage assets like power armors and waste valuable resources like energy weapon ammo on foes that were beneath the Brotherhood's notice, especially since, as some of the more senior Paladins point out, the larger towns and cities are perfectly capable of defending themselves with ballistic weapons.
Speaking of towns and cities, in a stark contrast as to how they are managed in Enclave territory, towns and cities in Brotherhood turf are mostly left alone, so long as they are mostly populated by humans. Similar to how many worlds in the 40K Imperium of Man are managed, many settlements have their own governments and ways of dealing with things, while paying simple lip service to the Brotherhood and occasionally sending out scavengers to find tech to trade with the Brotherhood for supplies. Some settlements have elections and councils, others have autocracies or a single magnate in charge. The Brotherhood cares little for how they manage things so long as things are peaceful, and so long as they keep the ghouls in line and turn over anyone who is a synth or a super mutant. This, of course, means that society in Brotherhood territory isn't as organized or as efficient as that of the Vegas Enclave's, especially since the Brotherhood gives little thought on developing communities and building up settlements, and worry more about scavenging tech and keeping it to themselves.
The Brotherhood's bias against ghouls, super mutants, and synths are still in full effect, especially since with the latter two, they were the enemies in the Brotherhood's past wars. Arthur Maxson still sees super mutants and synths as inhuman abominations who are a threat to humans, and those caught harboring synths or super mutants are considered guilty of a capital offense. They are either executed on the spot or enslaved by the Brotherhood by having them fitted with bomb collars and dispatched to help find tech in dangerous scavenging sites, with a Brotherhood agent ready to blow their heads off their shoulders should they run or resist. Ghouls are discriminated against and are kept restricted to ghettos, they are forced to register themselves and their communities. If they so much as insult a Brotherhood member, the ghouls can be shot on the spot without it being registered as a crime.
This explains why many ghouls, super mutants, and synths have been fleeing towards Enclave territory, where House doesn't care who they are so long as they serve him. Within Brotherhood territory, there is an "underground railroad" formed by super mutants, synths, and ghouls who have established themselves in House's lands, and they work to bring underground communities of ghouls, super mutants, and synths to Vegas Enclave territory where they bring their horror stories of being persecuted or hunted by the Brotherhood to the people of the west, where their wild tales become the stuff of movies and other media.
Enclave spies and refugees are also seen as persona non grata in Brotherhood lands. Just as Brotherhood agents are hunted in Vegas Enclave lands, so too are Enclave agents and remnants hunted down like dogs in Brotherhood territory, and civilians are paid well when turning them in. Remnants of the Enclave who were trained in the use of power armor and energy weapons are given one chance to join the Brotherhood, and if they refused, they are shot on sight or enslaved by scavenger teams with bomb collars. Enclave spies are captured and tortured before being executed. However, with the Legion training Frumentarii for the Vegas Enclave, the Brotherhood has a harder time ferreting out Vegas Enclave spies, as these Frumentarii are capable of infiltrating even the highest levels of the Brotherhood's command, with some even making it into Arthur Maxson's elite guard, giving House a good picture of what goes on in Arthur Maxson's court.
Basically, while the Vegas Enclave runs similarly to the Galactic Empire in Star Wars, this efficient bureaucracy that controls all cities and towns and has multiple groups pulling together under the leadership of one man, the East Coast Brotherhood runs more like the Imperium in 40K, where local settlements are rarely visited unless there's an actual problem the Brotherhood are interested in, be it technology, or fugitives from the Brotherhood's "justice".
This goes to show a real contrast in between the two systems, where the Brotherhood doesn't care what you do so long as you don't cross them, while the Enclave does care about who you work with, but they also care about protecting and helping you if you're on their team. This way, we don't just have two groups of idiots in power armor shooting each other, we have two groups that are ideologically different in every way. House and the Vegas Enclave sees reviving pre-war civilization as the way forward, the Brotherhood sees that as a folly and instead works with the new society of the wasteland instead of trying to turn it back into pre-war America. House wants to share technology and control everything, the Brotherhood doesn't care about control outside of keeping all the tech to themselves. The Brotherhood has a cultish view informed by their dogmas, while House is more pragmatic and looks to the future where he hopes to have the world cleaned up so he can go explore space for new worlds to colonize.