If OJ does not mind me putting in my 2 cents..
My experience is that Yes the .308 kills elk fine. I have killed a bunch of them with the little .308. The #1 thing that I see as favorable towards the .308 is that most guys can shoot them far more precisely than they can .338 WMs, or even hot loaded 30-06s.
Being well versed in precision shooting, in mountain conditions is far more important (in my opinion) than foot pounds of energy. I would not hesitate at all to hunt elk with a .260/.308 class cartridge, in a rifle that I can consistently shoot sub MOA groups with from field positions.
That said, I am a big fan of the .300 WM. It extends my practical range over the .308, especially when dealing with typical windy mountain conditions. Personally though, I require a brake on a sporter weight .300, in order to allow me to manage recoil better, thus allowing me to shoot it more precisely.
However, the .300 only really comes into its own when the ranges get extended.
When friends who want to "come out west" to hunt elk and mule deer start asking about what rifle they should buy, I normally tell them don't buy a new gun. Hunt with the precision gun that they are already used to, and have the most time behind. Almost all of them have a .308 in the stable that is set up somewhat similar to what they have used in their careers, and it only makes sense to have them rock a system they can operate at a level of unconscious competence.