I think the .375 as a medium, but have shot quite a bit with it. Things from steinbuck to giraffe weightwise, it works about as good for deer and elk sized animals as anything could. Bigger stuff included giraffe, eland and 3 buffalo. It's very useable for anything that a 30-06 trajectory will handle.
I used the .416 Rigby on buffalo, couple elephants, wildebeast, 2 impala with one shot and things like that. I'm teetering on the verge of wondering if it's worth it over the .375. I wanted it to kill better, but I'm not seeing it. Quite the opposite in fact.
I've got a .458 that I'm takeing to Australia in July, for a bit of a buffalo hunting and culling.