Both are good cartridges that have a lot going for them. Both will also work in a "standard length" action rifle.
I've hunted pretty extensively with the 9.3x62mm, and it is absolutely deadly on plains game. My father, cousin, and I have all taken numerous plains game with the 9.3x62mm and it performed almost perfectly. The cartridge is very accurate and reasonably flat shooting. The 9.3x62mm does meet the legal minimum in many countries for dangerous game, like Zimbabwe. I cleanly killed a cape buffalo and an elephant with it last year using 286gr Swift A-Frames and Woodleigh FMJs. However, I do agree with Winchestermodel70, it is a marginal caliber for dangerous game and you have a small margin of error in a charge situation. I will say that it does not give up much to the .375. If you can't do it with the 9.3x62mm, then you probably can't do it with the .375 either and will need to bring out the heavy artillery.
The .375 Ruger was a great idea and it performs very well in the fied. It does have a slight edge on paper over both the 9.3x62mm and the .375 H&H. But to get that additional muzzle energy, it is loaded to a much higher pressure than either cartridge which correspondingly increases recoil. The only other issue with this cartridge is that it is relatively new, being introduced in 2007 vs 1905 with the 9.3x62mm and 1912 with the .375 H&H. The older 9.3x62mm and .375 H&H have a much wider variety of ammunition available to choose from as a result.
This is just my personal opinion, but if I had to have only one cartridge to hunt with for the rest of my life, I would choose the 9.3x62mm. With the right bullets, it is an extremely effective cartridge on everything from deer all the way up to elephant.
