Any difference is just your familiarity with the rifle and cartridge, as at 600 the .375 H&H with Barnes 250gr TTSX is the literal exact match in drop and drift as the .338 Win shooting the much higher BC 225gr Barnes .338 TTSX. It is hard to imagine a closer ballistic contest, the .375 arrives with more bullet weight however, and at all ranges inside 600 where they meet ballistically a distinct numerical advantage. .375 still outperforms .338 Win no matter how we dice it, and while that's seldom necessary on this continent, it sure doesn't hurt anything eh?
-.375 H&H 85.56" low at 600 (100 yard zero)
-.338 Win 85.24" low at 600 (100 yard zero)