I have developed a great deal of faith in the .375 Ultra. I can't think of a land animal on the planet that its unsuitable for, given the correct load and bullet construction, yet with low velocity small game loads its no more destructive than a .22 LR, although this can be duplicated with nearly any centerfire cartridge. There are those who predict that Ultra-mag brass will become difficult to find, and that maybe true, but I'm not worried, I have lots.
The .378 Weatherby has a more dazzle than the Ultra, and it could be argued it will do anything the Ultra can do, while the reverse is not necessarily true. But I object to paying $6+ for each piece of brass, and the bigger cartridge cuts down on magazine capacity. That said, the .378 might well be my second choice to the Ultra.
The .375 H&H has capability and nostalgia going for it, sort of a .30/06-.300 Winchester analogy when compared to the Ultra. I got my first .375 Ultra with the intention of duplicating long barrel H&H performance from a 20" barrel. As it turned out though, the Ultra eclipses the H&H's performance even from a short barrel.
Then there's the .375 Ruger which has the appeal of the masses. As a choice for coastal brown or polar bear, when mated with the Ruger Alaskan rifle, its the obvious choice for such duty. A 260 gr Accubond at 2800 fps is tough to argue against if you're a bear.
Some decry the abandonment of the .375 Weatherby, and consider it the best of the breed. Perhaps they are right, but I have no experience with it, and the Ultra matches and exceeds the Bee's book performance.
I like them all, and could find happiness with any one of them, but the .375 Ultra is my top pick, and to my way of thinking is just a bit better.