You're better off using a .308 that you can shoot well than some giant howitzer that you're scared to death off. A lot of people make the mistake of buying a .458 recoil monster for brown bears and then they can't shoot it worth beans. I don't think I'd recommend anything smaller than 30-06 for browns, and preferrably something like the .300 or .338 Win Mags. If you're recoil sensitive though, just stick to what you're comfortable with.

Here's some good information from the Alaska Department of Fish & Game:

http://www.wildlife.alaska.gov/index.cfm?adfg=huntalaska.firearms

AK Jeff