I agree with 500Nitro and the others re 375 to 416 gap.
I shot a fair few buffalo last year with my 404, a few with my fathers 338 and a handful with my 300 Win Mag.

I would not recommend trying anything smaller than the 338 IF you are hunting alone and would be much happier with my 404 as I believe it stopped them a good deal better than the 338 and was SOOOO far ahead of the 300 that I may as well have sold it while I was living in the NT!

Keep the 9.3 as it has a good many advocates and a very strong pedigree to recommend it. It is also ahead of the 338 re bullet pen

Good luck and shoot straight,

MOG