All around the 375H&H is going to cover more bases for a "One rifle hunt" than any other cartridge in my opinion

If you are going to take 2 rifles you might stay with your 9,3 and add a 404 Jeffery or a 416 in Ruger, Remington, Rigby, Taylor or any shell that throws a 400 grain bullet at 2250 FPS to 2400 FPS.

Remember that the "Heavy Hammers" such as the hot 45s and the 500s 505, 577 and 600 are best for game that is already wounded, and are not billed as “standard hunting weapons”. They work fine for regular hunting, but in my experience, dead is dead, and the 577 Nitro will not kill a Buffalo much faster than a 375 H&H if the 1st bullet is placed correctly. But most men don’t practice enough to shoot the big guns as well as the medium size guns and therefore don’t shoot them as accurately. A well placed 404 Jeff is WAY better than a 505 Gibbs that hits “pretty close”

If you were backing up a hunter and only shoot when game was already wounded, then is when you would want to carry a “bigger hammer”

Speaking for myself only, I have no use anymore for rifles larger than the 404 and 416s, and in fact I would seldom take one of them when I can take my 375H&H.

But that's just me.......... Others may have different likes and dislikes.