I have been hunting bear and deer my whole life. My choice of weapons are 357 blackhawk with 158gr. jhp and 30 30 win. mod.94 sadle gun for bear. When I was a teenager in the 50s my grandfather shot a black bear that had climbed a tree and would keep the tree between himself and grandad. When grandad got a shot with his 45 colt he hit it between the eyes, you could see white bone for just a minute before it covered with blood. It took another shot through the lungs to bring it down.
I have shot well over 40 black bears and two griz. Almost always one shot kills. I can't imanage needing more than six 357 rounds to stop anything in north america.
I have never used anything but a rifel for deer.