Here in Wyoming we have 2 "classes" of predators to deal with.
#1 is what everyone deals with.
Coyotes, foxes, coons, skunks, feral cats and so on.
I believe the very best all around tool for dealing with these kind of animals is an AR-15 with a good scope.
The 2nd class has only one animal in it. Grizzly bears.
There are best dealt with using the most powerful arm you can shoot WELL. A good hit with a 270 is WAY better than a bad hit with a 458, but I am sure that's not news to anyone here. A good hit with a 12 gauge slug, 458, 416 or 375H&H is better still.
One animal that fits somewhere in-between and can be handled with either the big gun or the AR, or any other gun you can hit them with is wolves.
They would die about like any 100-150 pound dog would die I am sure.
Any rifle or handgun is ok for any animal on the list #1 list as long as you can make good hits with it, but some work easier and better than others.
I have killed many coyotes with 22 long rifles, but I prefer a 222 or 223. Predators are not usually eaten, and we are mostly concerned with "makin-um-dead" and not too concerned about how they get that way.