When I lived in Alaska, my job took me to remote parts of the state on a regular basis. Most of the time in brown bear country, I felt that a handgun was sufficient because an actual encounter was pretty unlikely. One of the guys I worked with only packed a handgun in with our equipment because he had a theory that luggage containing guns would get out to the villages on the same plane as us instead of being booted to the next flight. He usually didn't even bring ammo.
I did occassionally carry a rifle in some areas, and I carried a Blaser R8 in 9.3x62 Mauser and used the Kifaru gun bearer system attached to my pack in order to carry it. I like the gun bearer system for how quick it is to deploy, but it does take some getting used to.
Every time I have personally seen a brown bear, it was either running away or ignoring me from a distance. Moose, on the other hand, seem to appear out of thin air right behind you (except, I assume, during hunting season).