The 7mm-08 is a great cartridge. But, if you will take a look at the ballistics charts in the back of the Shooters Bible, I think you will find that the differences between it and the .308 Winchester are very nominal, both in terms of energy and in terms of "flatness" of shooting
The .308 has more footpounds close up, but the 7mm-08 ends up having a very small amount of extra footpounds down range.
Sighted in at 200 yards, the 7mm-08 may shoot 8/10ths of an inch flatter at 300 yards. So small that it is simply not worth mentioning.
They both have very moderate recoil.
I believe that because of this, you should select your round based on the type of rifle you want. If you are dead set on an autoloader, go with the .308. If you are happy with a bolt action, go with the 7mm-08
One big advantage of the .308 for big game: factory loaded cartridges with 180 grain nosler partition bulllets.
Best Regards,
Big Paulie