For practical purposes, there is no , ZERO, difference.
If you'll not, in the Berger Reloading manual there is a 200 fps difference between the 308 & '06 using Berger's 230 grn bullet.
If you look a little further, you'll see Berger used a 26" barrel on the '06 and a 24 inch barrel on the 308.
The difference is with that bullet, the '06 remains super sonic to 1000 where the 308 remains super sonic to 800.
That probably can be extended a tad if you used a 26 inch barrel on the 308.
For hunting, both have the energy needed to do what needs to be done to 500 yards, 300 being a reasonable hunting range.
We can play with a calculator all day showing one is better then the other, but again, what is practical.
Years ago, the army did some test on accuracy of the 30 cal bullet, working on loads for the International 300 Meter Matches. They found that the 30 cal seemed most accurate at 2200 fps.
I have target rifles in both calibers plus a 300 WM. In my years of shooting 1000 yard matches, the best score I've fired was with the 308 out of my M1A. But that was in perfect conditions.
So in reality, is one really better then the other??? Flip a coin.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071