how much of a practical difference is there to be made between a bargain basement barrel and some shmancy Faxon (or other luxury brand I never bothered to commit to memory), outside of weight via fluting?
unfortunately the answer, imho, is "depends on your shooting abilities". a quality barrel, in both materials and craftsmanship, is likely to mechanically outperform most human marksman's ability to use it because humans are inconsistent shot to shot without great skill, talent, or training. if we take the supposition that the ammunition and environment are "perfect", and the marksman is "perfect", then precise differences in barrel design, contour, rifling, material, length, et c will be evident and measurable, even if slight.
the human element is the one most subject to extreme and inconsistent changes relative to something like wind, quality ammunition, or a quality weapon, those differences in a barrel, while present, are greatly dwarfed by comparison. the average marksman is very unlikely to both notice the differences in barrel quality unless that difference is extreme, and is also unlikely to have the ability to identify that barrel's quality in comparison to another barrel.
as an aside, fluting is a way to reduce weight while retaining most of the stiffness/strength of the larger diameter barrel. it does very little for "accuracy" unless you have some sort of specific issue you are trying to resolve like barrel whip or something.
Shtf and you can never replace your barrel, what do you want to have? Chromed I guess? Guessing in that situation the accuracy gain via stainless wouldnt be worth the wear trade off?
well, let's have a brief mention of the technologies involved:
a chrome-lined or plated barrel uses chrome bonded to steel (4150 is typical but the alloy itself varies by the manufacturer) because it is very hard, very heat resistant, and is easy to clean with most solvents and provides excellent protection from general environmental damage with minor maintenance. it is difficult to achieve great accuracy with many typical chrome-lined barrels because the process itself adds material, and that additional material may not be completely uniform throughout the bore, which can create inconsistencies shot to shot where extreme precision matters. it is quite a step up from a plain steel alloy barrel and most of the way towards a stainless steel barrel, but costs far far less and can be turned around faster from the machine shop. 4140 and 4150 aren't all that super different other than when you get barrel blanks where 4150 is already pre-heat-treated from the foundry and ready for nitriding or nitrocarburizing if you want those. 4140 is a bit softer are easier to machine and if you are going to use something like melonite/QPQ you will want the softer material so nitrogen penetrates deeper.
a stainless steel barrel has a much higher inclusion of chromium directly in the steel itself (usually 416 of some magic flavor, but again it varies by the manufacturer) and while that avoids the issue of additional material from plating, you also have a different steel material that reacts a bit different to heat and corrosion. stainless steel will experience throat and crown erosion, just a bit differently in wear pattern and typically stainless doesn't have extreme resistance to this sort of wear - especially when is comes to flame cutting like at the cylinder gap of a stainless revolver. stainless steel often includes sulfur or phosphorus to ease machining, and your tools to make the barrel must be selected with that particular steel in mind. stainless steel often requires hand-lapping as the material is more annoying to machine precisely as the grain structure often is quite large, and while uniform and easy to make matte or brushed, a good polish without blemish is surprisingly labor intensive. these combined with the stainless steels typical for barrel making being somewhat expensive makes it a poor choice when the average shooter gets little to no benefit from using it.
given a situation where you will never be able to replace a barrel i would probably go with the stainless steel barrel. if you have the ability to care for the barrel and keep it in good order to avoid something like rust creeping in under the chrome plating, then a more typical 4150 chrome-molybdenum-vanadium (CMV) barrel would be more economical with few disadvantages. having put many hundreds of thousands of rounds down range, i never really saw much difference between stainless or 4150 barrels unless they were particularly prepared or had a special lining (stellite for example). 4350 barrels are a different beast altogether.