The .308 with premium bonded bullets like the Nosler Accubond or Partition, or the Barnes TTSX, is plenty for elk. That being said, if you're going on a distant trip to hunt elk and you might be faced
with a long range shot, then the .300 WM's extra range makes a
lot of sense. I'd probably go with the Nosler Accubond if the rifle likes it, as it's tough enough if you hit bone, has a good BC so it
maintains a flatter trajectory, and on a long range shot where it's slowed down considerably, the Accubond will still mushroom reliably.
I'd go with 180 grain. The .338 WM with Barnes TTSX's is what I'd use if I were hunting grizzlies or kodiak bears, but it's not needed for elk, and the .300 WM has a flatter trajectory. Hope this helps, have fun!