If I were being guided by someone like Phil Shoemaker I wouldn't worry about it BUT my thoughts would be ---- the closer the range the bigger bullet I'd want - that is, if the choice was between 180gr and 225gr I'd take the bigger bullet everytime.
The first brown bear I was while hunting on my own is Alaska was during a heavy rain in SE Alaska and he looked a VW with fur as he came out of brush at about 200 yards and walked along the beach away from me and my partner. We never got much closer before he turned and waded up a stream. I was carrying a .338 but I decided without that I wouldn't take a going-away shot especially with his fur being soaked with water.
Up until point I thought the .338 was the perfect rifle for Alaska but when I got to town I started looking for a .375 H&H which I used for the remainder of assigment in Alaska taking several moose, more caribou, a couple of very large black bear and a 9+ foot Brownie on the same beach on which refused the 1st saw.
And you know the .375 kicked a lot less than the .338 and it was quite a bit quieter.
The only reason I would choose the .338 or the .375 would be if I was into long-range shooting.
Your mileage may vary.
