If you are going to hunt plains game in addition to buffalo and only want to use one gun, I'd just stick with the .375 H&H. However, for buffalo only, the Lott would be great. I think calibers that begin with a 4 are the best for buff. But keep in mind, as several others have said, you're going to have almost half again as much recoil.
Just to throw a wrench in your thought process: I own both calibers but chose to use the.416 Ruger for my buff. I took the .416 and a .375 on that safari. I only used the .375 on three animals and used the .416 on the buff and seven other animals. The .416 kind of splits the difference between the .375 and .458 Lott and has a little flatter trajectory than the Lott with about 15 ft lbs less kick.
As someone stated, shooting at game you may not notice the recoil but practice is another ball game. For me, I can do about 24 .375 or 15-18 .416 but only about nine .458 Lott in a practice session. After that I start to feel like the gun's winning.