Jerry,
I have rifles in both 7-08 and 308. I have shot 3 elk with the 7-08 and none went more than 30 yards or needed a second shot. I have killed a pile of deer with both calibers and never noticed a difference in performance. I reload and just prefer the 7mm bullets hence my choice to use that for elk. If you don't reload you will probably have better ammo selection in 308 as others have stated. In my opinion though, there really is not much real world difference between the two.