I've always used 3.5-10 and 3-9 scopes on my .375s. The .375 is the epitome of a general purpose hunting rifle and the 3-9ish range is the epitome of a general do everything scope. Its a match made in heaven.
My first .375 was a 550, which got rebarrelled to .375 Weatherby after I shot it out. After playing around with 10 pound .375s for awhile I now favor a M70 Alaskan that weighs a bit over 8 pounds with a 3.5-10 Leupold. That's all a .375 needs to be.