To me, where you hunt and, to a lesser degree, what you hunt will determine what cartridge to use. The 338-06 and the 9.3 x 62 (I'm guessing this is the 9.3 you're referring to) are more versatile, especially the 338-06.

Assuming proper load development, you'd be set for all but the largest Plains Game, IMO, with the 338-06. This would be the best "compromise" out of the three you've mentioned.

I'm becoming more tolerant of intolerant people.