In terms of accuracy potential?  For example, using the same manufacturer and the same rifling technique and the same profile, is there a difference in potential?

As a side note, under moderate heat stress, would one or the other hold POI better?

Thanks!  

From what I have heard from ABS the carbon steel barrels may have slightly higher initial accuracy potential but when the throat starts to errode accuracy tapers off severely and quickly, as opposed to stainless barrels which gradually taper off over a much longer time.  

That argument in my mind for tactical weapons, suggests the superiority of Stainless.  

For competitors [probably bench rest only], the carbon steel may have a slight edge in it's prime that benefits the shooter.