Grizzly bears are relatively rare in number. They once existed throughout the entire western half of the United States.
Now there is less of them total than there is people in one small city.
So I wouldn't really recommend hunting them.
Having many such big predators actualy promotes a culture of carrying arms and helps RKBA. That it is a predator which is usualy easily avoided, yet has such a fearsome reputation makes it the perfect animal for the job.
I would rather be in the woods with such an animal than be stalked by a stealthy ambush predator such as a large Cougar.
Problems with the bear can be avoided through common sense, and if you do need to defend yourself you can react quickly. Problems with the cat are at the cat's discretion, and you probably won't see it coming.
If you have to defend yourself, the best caliber is a powerful one that you have with you. You don't get to plan defensive encounters, and by the time you have such an accidental encounter, you would have long tired of routinely carrying a cumbersome long arm with you during daily activities easier to do with two hands free.
So for hunting you want a powerful rifle for use at long range. For defense though you want what you will have on you when you finaly need it after months or years of never having an encounter.
I live in an area with a high tourist population and some people try to feed them. Thus the bear gets used to humans, and then the tourists leave and the bear tries to break into local houses and has to be shot.
Yeah many people are stupid that way. They want to save and support the rescue of animals, yet through human imprinting on the animal cause it to have conflicts with humans or not be afraid of humans leading to its death.
It happens with many types of animals. Both prey and predatory species. If you really care about an animal you want it as afraid of human beings as possible. Doing anything that causes it to either expect or depend on people for food, like with the bears and other predators, or causes it to trust humans like with many other animals, is a good way to cause its death.
It reminds me of people befriending whales and dolphins for example. I remember thinking how that was more likely to cause thier deaths when they travel into areas where people actualy kill them, than if the well meaning individuals had made them terrified of people instead.
The same goes for all animals. If you really want it to have a good chance of survival you want it to think human beings are the meaniest deadliest thing that ever walked the planet.
Animals can tell people they don't know apart as well as you can tell an animal of one species apart you don't know. Species learn to differentiate between members of thier own species, not others.
They don't understand hunting seasons, that people who they can learn to trust that merely watch them or point cameras at them during some months will suddenly be killing them in others.
That applies to everything, even birds you feed in your backyard. That same trust you cause the bird to have for humans is what gets it shot with a bb gun or slingshot by some kid in the next backyard, instead of it taking evasive action at the sight of them.
So the friendliest thing you can do for an animal is to use less lethal force on it and make sure it is absolutely terrified of people. Some rubber buckshot or bear spray at the bear foraging outside your home would be a good start (from the safety of indoors with lethal force also at the ready).
Of course those who 'think' they are animal lovers would think you were cruel, and might just encourage charges to be pressed against you for harming an animal not threatening your life if you did so. It makes no sense in reality, but does in thier own mind.
Can you imagine how tough it would be to bag a deer during hunting season if people were chasing them down with something like airsoft or paintballs the rest of the year? Those would be some of the most skittish and hard to shoot deer you had ever hunted.
The same applies to all animals.
Here is a bear that had about the nicest behavioral redirection possible, and was in need of shooting:
http://www.youtube.com/watch?v=_pLsM2ijRao
They should have sprayed it much sooner.
That might save its life in the future if it now fears people and associates them with a painful unenjoyable experience. It was obviously accustomed to people and a clear danger because of that.
Only some serious pain is going to make it realize hours of foraging for food in the wilderness is a smarter choice than getting the same amount of food in a couple minutes from garbage or human feeders.