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.