These are the type of discussions where every detail and clarification counts
Allow me to be very specific:
There is no arguing that a .416 400 gr slug delivers a harder blow than a .375 H&H 350 gr, however you care to quantify it: energy, Taylor KO factor, frontal area, mass, etc. It would be foolish to argue otherwise. This is obviously relative to the .416 powder capacity - not all .416 being equal - just as it is relative to various .375 powder capacity...
There is also good reasons to think that a .375 350 gr slug delivers a harder blow than a .375 300 gr, but this is less clear-cut: the 300 gr slug flies faster, and velocity being squared in the energy formula, a 300 gr slug technically delivers more energy than a 350 gr. However, a 350 gr has a higher Taylor KO factor than a 300 gr. As to penetration, the same mass vs. velocity applies. The 300 gr carries more initial speed, but the 350 gr carries more weight momentum. It seems experimentally established that in a .375, a 350 gr will penetrate deeper than a 300 gr of same construction. For example, Kevin "Doctari" Robertson, the well known and considerably experienced Zimbabwe PH and veterinarian believes that the .375 350 gr steps deeply into .416 territory...
There is also no arguing that a .458/470 500 gr slug delivers a harder blow than a .416 450 gr, however you care to quantify it: energy, Taylor KO factor, frontal area, mass, etc. It would be foolish to argue otherwise.
And when the game needs to be not only killed, but possibly stopped, this adds one layer of requirement on the rifle/load.
Therefore, for buffalo, elephant & hippo (rhino) a .45+ is superior to either .375 or .416,
because it penetrates and kills just as well (brain shots) or better (lung/heart shots), AND it also provides substantially superior stopping power. A .45+ 500 gr is a stopper; a .416 400 gr nudges the answer (and gets closer with 450 gr); a .375 300 or 350 gr does not.
As far as I am concerned:
1) where I can bring two rifles on a dedicated elephant hunt, my primary rifle is a .470 double, currently with iron sights, soon with Leica Tempus red dot, backed by my 1-6x24 scoped .375 H&H 350 gr R8 carried by a tracker, in case there is no other option than threading a difficult shot through a tiny opening in thick jesse at 50 yards, or if a dream 80 pounder cannot be approached at 75 yards or less (one can always hope!).
2) where I could only bring one rifle on a dedicated elephant hunt, I would bring a 1-6x24 scoped .458 Lott. I will likely sell my Mauser 66 .458 Lott and replace it with a R8 barrel .458 Lott...
3) where I could only bring one rifle on a mixed PG/DG hunt, I would bring my .375 H&H R8 with its two scopes:
--- one Leica 2.5-10x42 BDC sighted with 300 gr TSX for any PG and buffalo in herds, and 300 gr Partition for cats;
--- one Leica 1-6x24 sighted with 350 gr Woodleigh FMJ solid for elephant and hippo, with a handful of 350 gr Woodleigh RN SN (round-nose soft-nose) for hippo body shots, the RN SN and FMJ shooting to the same point of impact.
This would also be a great first shot / follow up shots combination for dagga boy outside of a herd...
This being said, many will argue that a single .375 with a single 300 gr load will do it all, which it generally will, although a "universal" expanding 300 gr will preclude brain shots on elephant and may prove less than desirable for brain shots at incoming buffalo or lion, should they be needed. Mercifully, I am not speaking from personal experience...