If I was arguing that the killing power of the 9.3 in modern loads was greater than the original loadings of the 375 H&H, I would look no further than modern bullets. Indeed that argument was available before modern bullets, at least according to Don Heath. I believe he had said the 9.3x62 was superior to the 375 H&H before the modern age because .375 bullets performed poorly. I believe he said they bent. I have to confess that I don't know where he said that but I am convinced that I read it somewhere, and in the history of firearms, such observations are commonplace. It could even come down to particular commercial loads, if they had a big bite of the local market he grew up in.
None the less, comparing modern bullets in 9.3, to traditional bullets in the .375 would probably give the 9.3 the win, even if there was no previous superiority in bullet design when the cartridges were fairly compared, side by side. And of course today, one can get great bullets in the .375s, so there is no cartridge superiority on that basis, and there are more choices for the .375. But on the simple question of whether the 9.3 of today is a better killer than the 375 H&H of legend, that is probably the case.