Too many generalities. Let's see if I can add a small amount of perspective here.
There are some cartridges that are harder on a barrel than others. Generally speaking, cartridges that burn alot of powder, yet use a (relatively) small diameter, light bullet....tend to produce barrel erosion at a faster rate than cartridges with less powder/ heavier, larger dia. bullets. The term often applied is "over bore" cartridges....as in, the case ( where the powder is) is MUCH larger than the bore itself.
The reason for this general characteristic of "over bore cartridges" is pretty easy to understand. More powder burnt, for a given bullet weight....therefore, greater hot gas induced barrel erosion. Smaller bullet....therefore higher velocity and higher levels of friction, as a result. Smaller bore, but bigger case.....higher chamber pressures, in some circumstances.
Now, the caveats - and there are a lot of them. This comparison, between "over bore cartridges" and more conventional ones, is real...but it does NOT operate in a linear fashion. In other words, you cannot do a direct comparison, based on some derived ratio, such as cartridge case dia. vs. bullet dia., etc. etc. There is A LOT more to it than that. I could go on, about 20 pages worth...and still not fully explain it. So, I will try to keep it simple.
So, for purposes of the OP's specific reference....the 308 Win. vs. the 6.5 Creedmore....which will wear out a barrel faster ? The answer is NOT clear. Simply going by the simple concept of the "over bore cartridge", as stated above, would suggest that the 308 barrel might last longer. BUT, there are LOTS of other factors....such as the specific loads used, the barrel composition, how many shots fired before letting the barrel cool down, etc. etc.
The short answer, on this question, really is : no one can say, definitively, when comparing two specific barrels - because there are too many specific variables.
But, in the real world, with cartridges loaded to the SAME pressure for comparison....and holding ALL the other variables as close to the same as possible... in many circumstances....the 308 would TEND to last longer. No guarantees, though.