I have never felt uncomfortable toting my .300 H&H around in big bear country, and certainly would have felt just as comfortable with a .270 Win or the like, even if I was actually hunting them.
I think I've only seen 10 or so coastal brown bears (NOT interior grizzlies: I've been around plenty of those), including one on Afognak that was a bit too close for comfort as he wanted my buddy's elk carcass more than we did.
Their toughness when shot I have no idea about, but concerning a charge they're nowhere near as aggressive as the interior bears (at least when not wounded), in my somewhat limited experience with them. I'd take Phil's advice and disregard everyone else's, if I were the OP.
