We have American elk here in NZ, we call them wapiti. Quite a few of my father's hunting friends hunted them in earlier days and in their opinion the wapiti were 'soft' compared with our prolific red deer. They dropped them no trouble with their 303's, 7mm's, etc, and this before the magnums came on the scene.
I haven't hunted wapiti myself, my nephew has, but I have certainly shot a lot of red deer and while the red stags are not overly hard to put down, red hinds can be. They seem to have a greater tenacity to life than their male counterparts.

I guess the elk in the States have some natural enemies such as bears and wolves which may make them more tenacious to life? Our wapiti, like all our big game animals, have no natural enemies so perhaps are actually 'softer' in nature.

Our hunters use their normal deer rifles. A friend of mine who was a government deer-culler used a 243 Win which he reckoned put down deer and wapiti nicely but he did go to a 30-06 when he started guiding hunters as he was shooting wounded animals in this scenario where hunters had fluffed shots.