I agree with pretty much everyone elses consensus. Both are nearly identical.
Advantages for 7mm-08 -
Slightly less recoil, very tiny bit of a flatter trajectory
Advantages for 308 -
Huge selection of factory ammo and it is cheaper than pretty much any other big game ammo, even if you handload, the .30 caliber has the largest selection of bullets to choose from
For me, I choose the .308, I have 3 rifles chambered in it and I dearly love them all. The availability of ammo is the deciding factor for me. Most people that I know that use the 7mm-08, all handload for it.