It is widely known that stainless will outlast CM...ie longer service life.
Can you verify that?
There are a lot of myths that are widely
believed. But something that is unproven cannot be widely
known.
As an astute previous poster mentioned, the categories of "416" and "Chromoly" are too broad for any meaningful comparison. If one chooses the extreme ends of the spectrum within each family, he could easily "prove" that chromoly is better than stainless, or "prove" that stainless is better than chromoly.
416 tempered and cold drawn is different than 416 annealed. Likewise for 4140 or 4150.
The critical property *I* would look at is the yield strength of the material *at temperature*. It's commonly known that 4140/50 has the desirable attribute of maintaining much of it's yield strength when hot. This is why 4140 is the default material for almost anything that must be strong when hot.
The highest Sy that 416 can achieve at a good temper is about 983MPa.
4140 with a heat treat and 540C temper can approach 1050 MPA yield.
So if you make a barrel from either material that is heat treated specifically for maximum yield strength, then the 4140 will have a higher yield strength than 416.
But then your gunsmith will complain about trying to machine 4140 or 416 at a hardness of 37-39 HRC. Not going to happen. Because smiths are generally more interested in easy of achieving good result than how long that result lasts.
Yield strength is important because it directly correlates to fatigue life. And fatigue life at temperature is what determines how much heat cycling a surface can take until it is fire cracking and checking.
One thing I've learned as an engineer is that there's no free lunch. Any material that has a particular advantage over another almost certainly has a major disadvantage to it as well.
Stainless obviously has the huge advantage of corrosion resistance. My experience suggest that the scales balance somehow-- Chromoly has some advantage are we'd use stainless for everything. Given that match grade barrels come in both materials at similar costs, you can conclude that machinability and cost aren't hugely different.
If I wanted a max-life barrel, I would go with nitrided 4150. Preferably a non-white layer gas nitriding process. Salt bath would be OK too, but not as desirable because of the brittle white layer that will break down with thermal cycles or impacts.(microcracking).
So what you can safely conclude is that the advantage of one material over the other really boils down to the tooling used to cut and form it. If the tooling is capable, the material can be harder and more durable. But with basic HSS cutting tools ubiquitous in the small shops of the gunsmith trade, you can all but guarantee that your barrel life is being sacrificed so the smith has an easier time machining it.
Heat treat matters more than what AISI designation attaches to a particular steel. If you are comparing steel grades without specificying heat treat, it's apples vs oranges.