IMO, .308 Win. is ONE of the best, for deer hunting, and not a bad all around round, either.
As for elk, I've seen quite a few who've fallen quickly to the .308, and my cousin, who is a good shot, practices, and is a good hunter, has not only killed quite a few elk with his Mdl. 70 Featherweight in .308, but pulled an Idaho permit for Shiras moose several years ago, and killed a really nice bull near Island Park, Idaho. Two shots, factory Fed. Premium 180 Nosler Partition.
The key is practice, being a good hunter and using the proper bullets.
FWIW. J.B.