I got to see brown bears up close (about 30-50 feet away) when I visited Alaska back in the summer. The sheer size and strength of them was both majestic and terrifying at the same time. If I had to pick a relatively easy-to-tote gun to tote in brown bear country it would be a lever action rifle in a something like .45-70 or stronger. IMHO even a S&W 500 would be marginal at best.
I own a .44mag Redhawk (loaded with heavy for caliber LFN ammo from Buffalo Bore) and have no doubt it would handle anything under 1000lbs. Brown bear in Alaska are a different story. My advice, if you want just a handgun in grizzly territory... I would say your EDC would be fine because you would be better off just sparing yourself the horror of being mauled to death by a grizzly. Sorry to be so morbid but having seen them up close, it's my honest advice.
Sic Semper Tyrannis