We hunt it all in the Arctic.
30-06 with 180 grn. soft points is THE all Alaska Cartridge.
Here, we all hunt year round, some more than others, but NONE even own a magnum.
The largest Bear hunting ,for Brown and Polar around here, is done with a 30-06 , 270, .308, and more often a 243.w with 100grn.
.243w with 100grns. ROCKS!!
.223 is a very versitile and much used round here. Not that great for bears, but most anything eles.
Bullet placment is EVERYTHING. If you can shoot it without flinching, and can keep your cool in front of an animal, then you will probly do very well.
Dont let Magnumitus blur your vision. Shoot what you can hit with(even if its a magnum).
Pistols are nice if your gathering fire wood, picking berrys, or fishing, but, If you activly hunting a Bear, Most guys here dont carry a back up pistol, they have a "Back up friend" who is also carrying a rifle........ though most will usually have a back up rifle in camp, incase one breaks, and they do. Bring a rifle if you want to "stop" a Bear. only a rifle or 12gauge slug will do that, so have a 'Reliable' rifle with you. If a Bear is charging you from the brush, its VERY unlikely that yuou will get off more than one round anyhoo.
Then again, you can bring Bearspray lube and take off the pistols front site.....
Like I said before,"If you cant kill it with a 30-06, you should hide."