Going back to the 375 H&H vs 9,3x62, I have both. A Winchester 70 pre-64 (1954) for the 375 and a BRNO ZKK 600 (1967) for the 9,3x62.
I have shooting and hunting with the 375 since I bought it, 1992, well used but well cared for, by a southafrican guy I never met. A lot more than with the 9,3x62 by the way! Looking at my records, the total shots with the 375 have been a little more than 1200. Yes, 1200. 95% at the paper and the balance in hunts.
With the 9,3x62, bought in 2017, I barely reach the 250...mostly at papers, of course, knowing the rifle and the cartridge and developing loads.
In my experience, they are different things. The 375 H&H has an "advantage" of around 200 f/s with all similar bullet weights, all other factors the same (Aprox. pressures and barrel lenght). Cannot be other way because the case capacity differences. Period.
Now, does this differences matter...? It depends of the personal needs.

Best Regards

PH