Just my .02: Bears, Cougars, Coyote, Wolf; I have taken them all. In 95 I got a bear peremit for AK, and got a really nice Brown Bear, after that I only refer to Mister Bear.
All of the above except bears die fairly easily Cougar (mountain kion) can easily be taken with a .22 if necessary. Coyote are smallish and a .22 or larger will do for them, although I have taken most of mine with a 30-30. Wolves I feel better with a 30-30 or shotgun W/slugs or buckshot.
Mister Bear is a very different situation. Obviously Black Bear do not need as much oomph as the Grizzley or Brownies. But all Bear have very hard heads, and their spinal cord is protected by heavy muscle and tissue.
When you talk Bear protection, you are talking about stopping a Bear not just killing him. For a bear attack, that is a charging Bear you need to get an effective central nervous system hit, that means brain pan or spinal hit.
First you have to be able to hit a very small spot(s) on a large animal (Brown/Grizz-very large) that is moving 20-30 mph toward you, and humping and swaying all over the place. Just a killing shot is not going to stop that animal, it must be precisely into the brain or spine, causing loss of motor control to the animal. Having the animal die a few minutes after he has claws on you is not sufficient.
Not only do you have to hit one of the two spots, your bullet must be able to penetrate to the right spot. This means a fast hard heavy slug, semi wadcutters seem to work better in handguns, and I favor a flat point for rifles and they seem to penetrate straighter and further.
I am not trying to scare anyone, my suggestion is that you do ANYTHING but face off against either species of Bear. If a Bear decides for any reason that he wants you, he is highly likely to be successful, there is always the chance that after a mauling a Bear might lose interest and leave, it has happened many times.
I am not so sure that "Bear spray" is not useful, it might confuse the Bear long enough for you to get away or place a number of killing/disabling shots.
Just my .02, I could be wrong, but I don't think so. Don't piss off any Bear, they can all get ugly rerally quickly.