My experience with elk thus far has been that most of us shoot far too much gun for a 150-200lb whitetail deer, as most of the popular "deer rifles" are right on the money for elk - such as the .308win.
Buffalo go a lot heavier, but for what it's worth, when I was a kid back home, if any of the wild buffalo herd we managed would get loose, the practice was to shoot them, rather than try to recapture them, and we almost exclusively used 30-30winchesters in Marlin and winchester leverguns. The two I've taken for sport have been with a .45-70, so not a LOT of difference in energy, but a LOT of difference in trajectory than a .308win.
BUT!!!!
Nobody should ever really need a good excuse to buy a mid-bore rifle. A 338win mag or a .375 H&H would be perfectly good selections for a mid-bore rifle, especially if large bears are on the menu. And of course, if you don't have a controlled round feed rifle in your safe, that's as good of excuse as any to add one.
