I have never hunted elk, so I don't have first-hand experience. However, a close friend of mine from Colorado has killed 5 elk (I've seen the photos) with a .270 Winchester--he grew up there. The .270 Winchester will do just fine. If it were me though, I'd handload my own ammunition w/ a Nosler Partitition or the new Accubond (which I've used on whitetail here in TX). The Hornady Light Magnum loads are excellent for factory ammunition.
Good Luck.