The caliber I would vote for that can cover all aspects of hunting big game animals is the .338 Winchester Magnum. Many years ago, I packed the 300 Win mag as my tool of the trade so to speak. However, their is a very distinctive difference between elk size animals that are hit with a 180 grain bullet from a 300 Win mag verses the more authorative SMACK of a 225 or 250 grain bullet from a .338 Win mag striking an elk or moose.
I have over the last dozen years or so, really noticed that big game animals, struck by a bullet from a .338 mag are more likely to show the hunter more physical signs of being hit. This takes away any after thought of a hunter wondering weather they hit the animal or not. I have hit elk using a 300 mag and wittnessed the animal run to the dark timber as though I missed completely. Now much to my joy I found that elk 150 yards away! Animals hit by a bullet from a .338 mag just don't seem to go near as far before giving up the ghost. This is my humble opinion of course, nothing is written in stone.