I do love to swing the big hammer. Killing is one thing, anchoring is another. That is another carry over from the long range game. How much energy are you delivering on target at those longer ranges. Also, being a veteran of a good bit of combat type stuff I am very much a worst case scenario guy. Gun fights are not won by the best guy, gun fights are won by the guy that screws up the least that day. While I'm sure charges and bad situations don't happen all that often I prefer to be prepared for such a situation and should it occur I would like to have enough rifle on hand to end it authoritatively.
And that is the path to the bottom line answer...
Kill a Buffalo?
.375 of any persuasion is about perfect as a client rifle because it has the penetration, the killing power AND it is easy enough to shoot for most clients to shoot it well, or at least well enough...
Stop a Buffalo?
Entirely different question!
The bigger (to a point! the shot MUST be true...) the better, but most folks will agree that it starts at .416 of any persuasion, includes the .458 Win, but really comes into its own with .458 Lott, .470 bolt or double, .500 bolt or double, etc.
Much ink has been spilled on whether stopping a Buff is a PH or a client issue. Being also from military stock and having routinely seen Murphy show up uninvited, I personally like to carry a rifle that would give me decent stopping power should the fecal matter turn toward the impeller...
What hunt?
I personally use an iron sighted .470 double because I am an incurable romantic and I like to hunt Buff up close and personal (call me dumb, but I like to keep the D in DG...). It is entirely perfect for me because I am single-minded on Buff when I hunt Buff, and, to be honest, I sadly do not have the opportunity to hunt Buff in places (e.g. Selous, Niassa, Luangwa, Grumeti, etc.) where the case suggested by Red Leg would be a reality...
But if you are out after buffalo with your .458 and a magnificent kudu rises from his bed on the next ridge at 250 yards ................
BUT... if I went on safari in places where it is likely to encounter the case suggested by Red Leg, and if I could not stay there long enough to be single-minded on Buff during Buff hunts, or if I was limited to one rifle, I would likely take my .375 H&H or my .416 Rigby. They essentially share quasi the same ballistics, although the .416 hits noticeably harder (see above comment about stopping power...). A very accurate S2 double 500/.416 with detachable scope would also be quite the ticket...
Overriding consideration...
A .375 H&H that a client is able to shoot reasonably well, beats any day a .416 or .458 that a client owns out of ego, is afraid of, and is incapable of shooting off hands into a paper plate at 50 yards...