I own both.

A 7mm-08 in a remington model 7, and a .308 in a ruger m77 stainless / syn. I have been hunting with the 7mm-08 for about 14 years, and the .308 for about 6 years.

Both are effective on deer sized game. The model 7 has a 20" barrel, and is a compact rifle, so it would not be much different than the rifle and barrel combo. you are considering. They both are effective on deer ( and I have taken deer with both ) out to around 400 yards, even with the shortened barrel guns and their loss of velocity. The 7mm-08 being lighter has recoil about equal to the .308, but neither has bad recoil. So just about everything comparing the two , is a wash.Both are capable of dropping a deer in its tracks.

The biggest difference between the two is the choice of factory loads available. The .308 has more choices of bullet types and weights available for it than the 7mm-08 does, but if you wanted something easier shooting sometimes, the .308 is also offered in the remington managed recoil and the federal low recoil ammo. This ammo uses a lower powder charge and a bullet designed to expand at lower velocities to acheive the lower recoil which is slightly under that of a standard .243. This ammo also retains enough terminal energy to be effective to just over 200 yards. This makes it a great round if you think you want to shoot something easier, or if a woman or child might shoot it.

If you were going to corner me up on a decisive answer, while I absolutely love my rem. 7mm-08, I would give the nod to the .308 round, simply because of the expanded choices of ammo types available.

I hope this helps and answers some of your questions.

God Bless