In a modern rifle with a long barrel of 26"s and a warm but safe handload the 9.3x62 will equal the 375 H&H and the 9.3x62 for all practical purposes...My 9.3x62 Buff load is a 320 gr. woodleigh soft or solid at 2400 FPS plus just a tad or the 300 gr. Swift at 2450...My 375 H&H pet load is a 350 gr. Woodleigh at 2350 FPS or a 300 gr. Northfork at 2500 FPS...

Your question referred to the difference in game killing...I have never seen any difference in the three of them and I have shot DG with all three. I quit using the 9.3x64 because my 9.3x62 was lighter and killed as well..But be sure the 9.3x64 is one heck of a great caliber.