I've owned both a d killed plenty of game with both and came too two conclusions.
The 375H&H has more legs for 350m shots but has noticeably more recoil but it does have more power.
For 250m and under shots the 9.3x62 is noticeably more pleasant to shoot, I think of it as having 1/2 the felt recoil for 3/4 the power, but it is more of a rainbow trajectory.
For my hunting the 9.3's make more sence and I love the 375H&H.

Under 200m there isn't an animal on the planet that could tell the difference between them, both will do the same job out to that range.