I don't see much practical performance difference between the 308 and the 7-08 with 140-150 gr bullets.
Up to 200 yards, hard to beat the old 308 if you want practical, and the 243 for comfortable. I think recoil sensitive people may shoot the 243 better than the larger cartridges.
Deer are not that hard to kill, listen to the guys using 223's on them.
I always shot 150 and 165gr bullets in my 308's. A friend of mine swears by the Sierra 125 gr Spt bullets in his 308. I don't know why a 308 shooting a 100-130 grain bullet wouldn't work as well as a 257 Roberts, 260, 6.5x55, 270, 7-08, 7x57 shooting the same weight bullet on deer?
However, just to be even more practical, the boring old proven 270 with a 130gr bullet is pretty awesome on deer. Reload inform and cartridges everywhere. Besides the 270's are the true 7mm's.