Welcome to the madhouse Sheldon, where you are sure to receive the benefit of candid, unvarnished, and generally very experienced opinions grounded in cumulative decades if not centuries of actual African hunting experience.
A few immediate thoughts come to mind as you start your new quest...
1) Yep, a .375 H&H slug in the right place beats every time a .40, .45, .47 or .50 slug in the wrong place. But you know that already... This is worth saying though, as
Ridgewalker states, that not everyone shoots happily (and accurately) the big bores. Nothing about manhood, mind you
, just that different folks are affected differently by different levels of recoil. Nothing worse than a rifle that hurts you and that you are afraid of. There is a good reason why the .375 H&H has been recommended by Professional Hunters (PHs), and mandated by most African Game Departments, as a sensible minimum caliber for dangerous game for visiting sportsmen for a century. It is about the best compromise between lethality and shootability. European friends may prefer the 9.3x64 (if they can still find it) and the 9.3x62 is not all that far behind...
2) This being said, and as well as the .375 H&H kills Dangerous Game (DG), even its most ardent defenders, and there are plenty of them, will grudgingly admit that the .40, .45 and .47 hit them a lot harder. This is the reason, by the way, why very few PHs use it as their choice to back clients on DG. Does it make a tremendous difference for a first shot with good presentation at an undisturbed buff? Maybe not all that much. Can this be significant for a stopping shot at a wounded fleeing (or charging?) buffalo with a less than perfect angle? Likely. But only if you place the bullet in a reasonably good spot, hence only if you can shoot the dang thing... And keep in mind that your job as a client is to do everything possible to make sure their is no need for stopping a wounded buff - as in: shoot your rifle straight when you open the ball.
3) Then there is the issue of how many rifles will you take to Africa and what will you hunt? Buff only or buff/plains game combo? If the answers are: only 1 rifle and mixed bag of plains game & buff, then the .375 H&H is probably one of the best compromises. But keep in mind that the .416 Rigby (Rem etc.) and even the .458 Lott shoot about just as flat as the .375 H&H out to 200 yd, so they too can pretty much handle anything ... if you can handle the recoil... An interesting compromise (if you can find one) is the .404 Jeff. It hits definitely like a .416 (well almost, and so close that it is not worth splitting hairs) and it recoils not much more than a .375...
And so it began... Welcome to AH! For what it is worth, I have personally dropped off the .375 wagon some years back and I carry a tuned-up .416 Rigby (CZ) when I do not carry a .470 double (Kreighoff), which I do more for sentimental than practical reasons I will hasten to admit...