I would use my 300 H&H on about anything, if I get to use the bullets I want.
I have other rifles I might prefer for some hunting, but I can't think of any game I would be unwilling to shoot with my 300 H&H, up to and including elephant and hippo. The "trick" is to turn down shots that are not perfect. That can be exasperating and expensive in today's economy. (that's why I would choose other rifles some times) but if I could use 165 gr Barnex X, 220 grain Nosler partitions and some good 220 grain mono-metal solids, and if time and money were not objects, I would gladly take a 300 H&H for any game I can hunt.