One reason i've always liked the .338 Win mag. over the .375 H&H mag., is because the 338 rifles weigh less!
The .375's have "varminter" weight bbl. with a .375 hole in them, the .338's have "sporter" weight bbls with a .338 hole in them. I like the "less" total weight of the .338 rifle, as i have to pack it all day long.
Another thing, i can load 200 grain bullets in the .338, and that lowers the recoil considerable, but it still plenty of bullet for caribou, blk bear, deer ect...