You go up in bullet diameter to gain bullet weight not diameter generally. The difference between .338” and .366”, .028”, isn’t making one iota of difference in terminal effect. Both the .338 and 9.3 sling equal bullet weights, the .338 just has more options and better BCs. Of the two, it’s more versatile as it can handily be a mountain sheep rifle, or a bison rifle, and effective from 10 to 1000 yards. Not saying just anyone with a .338 should shoot game at 1000, just that a .338 Win will do that better than most.
The one place the 9.3 wins for me is Africa, as the 9.3 is permitted on dangerous game in some jurisdictions. On blast there really isn’t much difference between a 20” .338 or a 9.3, both are loud, the .338 isn’t a big magnum or overbore. I don’t own a .338 but respect the round, it’s a heck of a North America cartridge for all round, long mountain shots included.