Shot placement is probably the most important thing to consider. I have seen several 1,000 lb plus bovines put down with one 22 cal shot to the head. In the old days, lots of game was put down with firearms that would be considered way underpowered by today's standards.
I often wonder about folks who are buying 7mm & 300 Win mags to shoot antelope and deer. To cover up poor marksmanship? I was at our local sight-in days (a few days to help out of town hunters check their rifles) and watched a tyro with a 7 mm empty a box of shells at a target. He didn't even hit the giant target frame, let alone the target. He said, "Hell, that's close enough". I guess he thought the extra power would cover up poor marksmanship and still allow him to bag his game.
I hike the Bighorn mountains on a regular basis. I haven't carried but have considered it but I'm not really worried about animal attacks. I think we have more to worry about with humans. We have a few bears and way too many mountain lions, IMO. Hunter's have killed several mountain lions within a few miles of my house and I've had tracks in my back yard. But, with mountain lions, you'll probably never see them coming as they sneak up behind you and snap your neck. Wearing a backpack might save you but you still have lots of problems if you survive the initial attack. I guess I think, as long as the lion is putting the hurt on me, it might be nice if I could draw a weapon and put some hurt on him before I die.
I don't think I've ever heard of anyone being attacked by wolves or coyotes. Wild dogs are a different matter and I have come face to face with two pit bull looking dogs while hiking with my wife. I had no gun or pepper spray and I was pretty darned nervous, especially for my wife. I felt pretty helpless and might just decided to carry for dog and human risk factor.
Cloudpeak