NitroX makes a good case for the .375. I have used my Sako .375H&H with 300 grain Barnes TSX to take a warthog and an Impala. The impala went 50 yards after a textbook perfect "quartering to" heart/lung shot, and the warthog was a bang flop and didn't take a step. Meat damage was not extensive on either, thanks to the hard bullet and moderate velocity. I only carried the 300 grain bullets because this rifle was my backup rifle on a Buffalo hunt but the big slugs worked very well on the smaller game.

I don't think the .375 is at all overpowered for smaller medium sized game, and I believe it is quite effective, although one could argue for using something in one of the more pedestrian 30 calibers or less to great effect without having to deal with the recoil of the .375. On the flip side, the .375 will scale upward. Although I have not had opportunity to personally do it, I would feel comfortable with a .375 for broadside buffalo, as well as large moose, eland, etc.

IMHO the .375 offers compromise on both the small end of the scale as well as the large end of the scale. Is it perfect? Nope. All compromises are just that: a compromise. But the .375 is probably the very best compromise available to hunters in the past and today.