I never know what kind of game I am going to encounter, wherever or whenever I hunt. Any animal weighing over 150lbs, when in the wrong frame of mind, can become bellicose and dangerous. For this, as well as other reasons (such as unpredictable, difficult shots), I hunt with a .375H&H loaded with 300-grain softpoints - always.
In Africa, dangerous game is encountered most often, whether they be part of the big 5 or just some other cantankerous critters such as hippo, croc or zebra, who decide they don't like the cut of your suit. And the overwhelming choice among African professional hunters is the .375H&H, both as a personal choice and as a recommendation to clients.
A friend of mine and prominent South African Bwana has explained to me that the .375, unlike the 416s and the 458, is very easy to shoot by the average hunter, and is less likely to cause a nervous client to flinch when the chips are down. He therefore prefers to see his clients armed with the old H&H than with any of the more modern and potent fodder such as the Weatherbys.
Even Craig Boddington, possibly the most literate of modern-day experienced hunters, has tallied the .375H&H as by far the most recommended cartridge for anything larger than medium plains game in his must-read tome Safari Rifles (Safari Press, Long Beach CA, 1990).
In my less rembunctious years, I have come to lay down the old .416 in favor of the .375, which I would not hesitate using on any game on Earth. I have come to learn to place my shots with surgical precision (as far as it's possible) and the gentle shove of my 9 1/2-lbs rifle has become second nature.
I have not yet had a use for solid bullets, though. I think that their need is very limited. Brain shots on elephant (hardly a commonality these days) and body shots on rhino (ditto) are the only 2 instances in which I would use them. Thing is, that controlled-expansion projectiles have gone such a technological distance by now, that with them you still get plenty of penetration plus expansion and hydrostatic shock. The Trophy Bonded, for example is a helluva lot of bullet, as is the Hawk and, of course, the Partition.
If I had to face a charge, I would much prefer a good, controlled-expansion 375+ bullet than any solid on Earth, possibly even for elephant. Put such a slug in an animal's puss and you'll turn it at the very least. Instead, a solid could even go clean through (especially with a soft-skinned animal such as lion or leopard) without making much of an immediate impression.
This is just my opinion, and I bow to any of you more experienced hunters out there, but so far I have not been disappointed. I am thinking of re-barreling one of my .416s to the 450/400 Nitro Express, and see if I can unseat the .375 as my King of calibers!