Again, no one has said that handguns are the best tool for the job. However, it is a proven fact that they are capable if the shooter is
I don't know any shooters who are. Real brown bear attacks (as opposed to those who stupidly shoot bears that growl at them) are sudden, silent rushes from close range. If you are in dense cover (where these attacks generally happen) your shotgun (or Marlin) is in your hands. I've been in that situation twice. Once I got mauled in absolutely horrific circumstances. The other time I shot the bear in the face and stopped it right there, 5 yards from where I was standing. I'm batting 50%...
On at least a dozen other occasions I've faced down brown bears going through the typical "threat display". This situation is what most tourists think is an attack, but is really just (as described) a display. When you have that warning, the bear has no intention of attacking. It's like a rattlesnake, just warning you off from its day-bed, a kill, cubs, whatever. If you get a warning, you're in no real danger. Just heed the warning and back away.
I've been there and done that. When they come for you, they'll creep in or just spring from their bed with no growls, no warning, just 600 to 1000 pounds of bear bounding at you at 40 mph from less than 20 yards. If your shot (and you have about 1 second to make that shot) goes through their nose or mouth, you'll stop it. A body shot, or a miss,
might turn them or it might just make them angrier and turn a swatting into a killing.
The bear I killed was with a Marlin Guide Gun with Wild West ghost ring sights. Everything was in slow motion, but that fire-dot front sight seemed to waver around forever before that red dot was on the face. I slapped the trigger and the bear crashed. It was just a small bear - a 3 year old that weighed maybe 300 pounds. I got lucky.
I was already gun-shy after the mauling, and the second episode made me decide a shotgun was a better answer. For me, I've been shotgunning since I was 12 so it's instinctive to throw that gold bead on a rabbit or ptarmigan - or a bears face. I experimented with different slugs, snap shooting targets at ten yards or so. I found that
with my shotgun, the old foster slugs shot to point of aim, and the various sabot slugs didn't. Your mileage, with your shotgun, may vary. But, they must hit point of aim. If you have a shotgun with adjustable sights, then you have some latitude.
If you can turn, draw, and hit a softball with a handgun skipped from 20 yards, then fine. I can't do that, and I don't know anyone who can. A shotgun is designed for snap shooting. In my opinion (and I've been there), it's the best choice for most people. Jerry Miculek, excepted.