My response hinges on what type of bear you are hunting:
1)Black bear can easily be taken with a 200-225gr load with any premium bullet(Barnes-X,Trophy Bonded, Swift AF, etc.)
2)Inland grizzly, I would lean more towards a premium 250-275gr load.
3)For the big boys, polar and coastal grizzly(Brown if you prefer) I personally would use the .416. However if I were to use a .338 I would use those mentioned in #2 above.

Six years ago I took a Brown in Kamchatka, Russia. These bears are genetically identical to Alaskan Kodiacs. I took a .416 Rigby as my primary gun and a .338 as a spare. I'd just like to say that for these bears a .375 or .416 is about ideal. Craig Boddington had just hunted with the same outfitter a few weeks earlier than I, and took his bear with a .338 Win Mag. I saw him at the SCI convention a few months later and he confided that he would have felt a tad more comfortable with a .375. These bears average 850-1100 lbs!

Geronimo