I have been mentioned twice in this thread so I'll add my five cents worth. There is, in my opinion a logical explanation why the 9,3 x 62 mm, and well-constructed 286 or 300 grain bullets is such an effective, dangerous game combination.
It is simply this:- this ballistic combination is wonderfully 'shootable', which goes a long way towards ensuring initial shot placement is good. Knowing your rifle/ballistic combination is 'marginal' for buffalo, also seems to have a physiological effect - which in a way seems to improve ones shooting performance.
I have yet to meet an enthusiastic dangerous game hunter who could not shoot my 9,3 well, and this includes quite a few from the fairer sex. I have however encountered quite a few 'with hairy chests' who were 'scared' of a .375's recoil.
There are three components to 'recoil' - the force that comes back into your shoulder measured in foot pounds (Free Recoil Energy), the speed or velocity with which this force is delivered (Free Recoil Velocity measured in fps) and the 'duration' of the recoil event.
Recoil starts the moment the bullet starts to move out the neck of the cartridge case and into the freebore and it ends when the bullet exits the muzzle.
A 10 pound 9,3 x 62 mm firing a 286 grain bullet at a muzzle velocity of 2350 fps (or a 300 grainer at 2300) creates a FRE value of 28 ft pounds at a FRV of 13.5 fps.
A similar weight .375 H&H firing a 300 grain bullet at 2550 fps of muzzle velocity creates 41 ft pounds of FRE at a velocity of 16 fps.
I do not have a figure for the duration of the recoil event but given similar barrel lengths the time it takes for a 286 grain .366 bullet to be accelerated to 2350 fps is longer than it takes a 300 grainer to reach 2550 fps.
Put simply, a similar weight .375 H&H recoils 50% more than a 9,3 x 62 mm, and this 'experience' is delivered over a shorter/sharper time period, all of which translates into a very different, more unpleasant shooting experience.
This makes the 9,3 a lot easier, more pleasant, more manageable call it whatever, to shoot. Pretty simple really, all of which contributes significantly towards 'confidence' which in turn equates to better shooting and correct first shot placement.
I have more than three decades of 9,3 experience and I long ago realized that 300 grain .366's (at 2300 fps) seemed to me to be more effective than 286 grainers going a bit faster. I attributed this to a better sectional density, .320 as opposed to .305, and a slightly improved momentum value - 99 pound fps to 96.
More importantly, the 300 grain expanding bullets I used for decades, flat nosed Hi-Performers made especially for me by the late Ken Stewart, had nice, 2 mm thick jackets and bonded cores, and they expanded reliably to a little over double caliber in size which created nice and big wound channels which resulted in turn to quick deaths when these bullets were placed into the heart/lung area.
Many buffalo are shot from the frontal angles where the inch-thick frontal chest skin of a buffalo is a formidable obstacle for any bullet. I quickly became convinced that from these angles, an expanding 300 grain .366 bullet at 2300 was more effective than a similar 300 grain .375 bullet at 2500 fps. Higher SD bullets at a lower mv overcame the 'trampoline effect' of the frontal chest skin better/easier than lower SD bullets going faster. In such instances, momentum, in my opinion, is a lot more important than energy.
Along with my Brno ZG47 9,3 x 62 mm, I also owned for a time a Browning A-Bolt Medallion .375 H&H. This rifle weighed only 8 pounds and my clients used to complain bitterly about its recoil when full house factory loads with 300 grainers were used. To get around this I used to reduce the mv with 300 grainers to 2350 fps. Not only did this reduce the recoil, but it also improved the terminal bullet performance. When 350 grain .375 bullets became available (and 380 grain Rhino's) this bullet weight elevated the .375 into another performance class altogether - but this is not the topic of this thread.
The 'nine-three's' work because they are the easiest of the DG suitable combinations to shoot, and when bullet placement is where it should be, they 'work' surprisingly well.
There is an old saying - 'shot Placement is the best caliber/cartridge combination' and the 9,3's are the easiest way to accomplish this - pretty simple really!