RE: brown bear caliber
Can't answer from experience since I've never killed a brown bear. But if I had the coin to book a hunt in AK, I'd stoke my Ruger No 1B .338 WIN MAG with 225 grain Barnes Triple Shock bullets, sight it indead on for 100 yds, practice once a week at the range in several shooting positions, and buy extra life insurance to give to my kids in case I shoot poorly!
If money were no object, I'd have a .50-110 a.k.a. .50 Alsakan built and take that on my hunt. The I'd have a lifesize mount done and while the taxidermist is taking his time, I'd have my game room rebuilt with 12ft ceilings so I could fit that bugger in there!