I wonder if you are referring to the .378 Weatherby, which is the .460 necked down, or to the .375 Weatherby, which is the .375 H&H blown out. The .375 is a dead issue, and although you can shoot .375 H&H ammunition in it safely, the resulting performance is lower than the original .375 H&H.

The .378, which is basically a .416 Rigby necked down with an unnecessary belt added, gives you a slightly flatter trajectory at the expense of far greater recoil and much more expensive and difficult to obtain ammunition.