Truth be told, you really aren't giving much up in performance or power to the .375 by using the 9.3.
That being said, the cartridge is not legal to use on dangerous game in many countries in Africa that require a .375 caliber minimum. If I were a PH for dangerous game I would not use the 9.3 or even a .375 for that matter. I'd use a much more powerful cartridge like a .416 Rigby, a .458 (Winchester or Lott), or something even bigger if possible if I needed to go toe to toe with elephant and buffalo on a regular basis.
I think most would agree with that. As a PH, I'd want a "stopper", .450 #20 NE double would be my first choice.