I own and like both calibers. I think it's a bit easier to get a .308 to shoot small groups than a 30-06, but not by a lot, and I have a couple of 30-06's that shoot sub MOA groups on average. I do have a slight preference for a 30-06 as an elk rifle because it has a little more power and a slightly flatter trajectory. But either cartridge should work just fine. It really comes down to personal preference.
