Well, the 308 is the 7mm-08s parent case (this is sorta like comparing a 30-06 to a 280). Obviously, one shooting 30 cal bullets and the other pushing 7mm pills. They're both good cartridges for deer, and shooting proper bullets would both be suitable for elk (though I might opt for a touch more oomph there, if given the chance). The 308 probably has more factory ammo choices, and probably has some availability of cheaper ammo, not sure on that. The 7mm08 recoils slightly less. Both are known for "inherent" accuracy by case design. Basically, two capable cartridges. The question is, do you want to shoot a 308 or a 7mm08? That's about all you could ask a deer hunter when it comes down to it.