BoS were opposed to others having advanced tech because their founder was disgusted with scientists performing freakish experiments on prisoners at the military base he was stationed in, so he decided that BoS should safeguard technology so it doesn't fall into the hands of people like Caesar ever again. Enough time passed that BoS forgot the original intent and devolved into more of a cargo cult stereotype where they hoard tech for the purpose of hoarding tech. In Fallout 1 they're literally Knights With Guns, as Fallot 1 was pretty much Pool of Radiance With Guns, all the fantasy tropes are there - paladins, wizards (scribes), shining armour (power armor), elders, knight errantry (the Glow quest), you get it.
To be fair, the BoS is still trying to keep tech from the hands of guys like Caesar and the NCR when you meet them in FNV. And in Fallout 4, they're trying to wipe out the Institute scientists who were experimenting with cloning humans and making Synths. So they're still doing what their founder asked of them. It's just that they have no real vision or purpose for what to do with all that technology; they never did. They're not preserving civilization like Caesar is, they're not preserving American democracy like the NCR is, they're not preserving the American state like the Enclave is, they're just hoarding for the sake of hoarding, because the founder knew nothing else to do with all this tech and power, and nobody else did outside of the Lyons clan. And all old man Lyons knew to do was to make his Brotherhood into a local town guard.
Meanwhile, Nod actually had a vision for the future and a desire to create a unified state under their leader, with a philosophy of universal brotherhood, overthrowing wealthy oppressors, and helping the downtrodden by any means necessary. If Nod existed in the Fallout universe, they'd go to war with the Enclave and the NCR because the rich and the powerful dominate both sides, hoarding resources for themselves while letting the poor rot. They actually have a philosophy that goes beyond just hoarding tech (in some cases, Nod invents new tech as they go along) and they have a leader who has a long-term plan for humanity and surviving a poisoned world. It's just that said plan is going to get a lot of people killed in the process, and he's OK with that.
Nod has almost nothing in common with Brotherhood of Steel aside from maybe technophilia.
They're both technophile, quasi-religious, military order-states fighting against an American-style government; the GDI for Nod, the Enclave/NCR for the Brotherhood of Steel. They even have heavily-armored troops leading their forces; Paladins for the BoS, Black Hand/Enlightened for Nod. They both use laser weapons and all manner of advanced weaponry, whether it's small arms or big. They both field large robots; Liberty Prime for the Brotherhood, and the Avatar/Redeemer war-mechs for Nod. It's just that Nod is more successful and has no problems using genetic experiments or cyborgs to win the battle, and they actually have a political vision for the world, whereas the BoS are just hoarders who ignore the outside world while sitting atop their pile of scavenged or stolen tech.
Last we checked, the BoS is decaying in FNV and its fate in FO4 is unclear, whereas in Wrath of Kane, Kane succeeded in grabbing the Tacitus supercomputer, and Tiberium Twilight shows that Nod and Kane accomplished what they sought and ascended to some mythical la-la land while leaving behind a clean world for their former GDI adversaries. So even their enemies benefitted from their shenanigans in the end, whereas the only way you can do that in FNV for the BoS is if you marry them to the NCR by way of a peace treaty, so they can fight Caesar's Legion together.
