I did contract work as a trapper/predator controller for Colorado Division of Wildlife (before they combined with Parks dept). I carried a .50 Hawken . Not because I had to, but because the rifle was a tack driver out past 200 yards loaded with .490 round ball, patched with a .010 patch coated with 50|50 bees wax and buffalo suet, and pushed by 90 grains of FFg. I'd had it for years after I built it, and was VERY familiar with it, and I could shoot about 100 rounds through it for about the same cost of a box of 20 rounds for my .30-06, and less than a box of 20 for my .300 Win Magnum.
During the years I contracted with them, I shot coyotes, fox, bobcat, cougar, and black bear. For myself during that time, I shot jackrabbits, cottontail rabbits, mule deer, elk, cougar, coyotes, and black bear.
I found the rifle to be plenty good medicine for any of those critters. It's all about shot placement, and realizing that a round ball has no shock power (kinda like shootin a bow). For backup, especially for dangerous critters, I carried a .50 CVA Mountain Pistol that I built from a kit. I loaded it with 90 grains FFg and a 375 grain Maxi-ball. Kicked like a mule, but was definitely good for close work.
A body can certainly go bigger caliber if it makes you feel more at ease, but I always found that a half inch hole was plenty big to properly ventilate hearts, lungs, livers, or brains. I even ventilated a few spines. I'm kinda partial of goin after the boiler room unless I'm right on top of em. Then a brain pan shot does the trick great.