To me the single greatest difference is availability of "quality" ammunition. The 8 X 57 is largely a handloader's proposition as factory loaded ammo for the German round isn't up to the standards one can handload. In this arena the .308 wins easily. and if it's ever happened that you are 1,000 miles from home and need ammo you'll have a much easier time of it if you are looking for the .308.

I hunted elk with a friend once who bought along his .35 Whelen and errored in bringing ammo for his .300 Win Mag by mistake.....we searched all over Denver for .35 Whelen ammo and never found a single round.....it's unusual but it does happen!!

To me it's the single greatest reason to own a .30-06, a .308 Winchester or a .270 Winchester.....good quality ammo is likely avalable in Podunk Iowa if need be.