I'd go with the .338 in the Ruger.....partly because of how I like those very strong rifles, and partly because the .338 with the right projectiles is more appropriate to the game you will be hunting most of the time.
I've never hunted buffalo, but believe that if the .338 ammo' meets the manufacturers recommendations for buff' then it is the better choice. The weight and construction of the bullet would be the key here. I'd go with the heavy-for-caliber projectiles for buff', and with the mid-weight projectiles for large elk and black bear. For grizzly I'd try a premium bullet, actually.
The .338 certainly is a more versatile caliber for use in the lower 48 states, including against grizzly if you ever do that one day. The .375 H & H magnum is just too heavy in the recoil department, and lugging around a heavy rifle to tame it just wears out the hunter. Why bother?
I'd get the .338 and never look back -- if the ammo' meets the requirements for your game.