From time to time this has been reported for various cartridges, including the .375 and the .270. IMO it has to be related more to the rifle and it's barrel/stock fit as well as how it is supported than the case itself.
Normally a heavier bullet will print higher on the target at 50 or 100 yards, due to higher recoil and longer barrel time. At longer ranges this eventually reverses. In the case of two different bullets like your .375, they may print together at 100 yards, but they will not at 300. Still, this can be handy for the hunter who wants to carry two different bulelt weights for the same rifle. However, I can only think of a couple of reasons why he would, and they involve hunting in Africa and Alaska where dangerous game can be encountered while hunting more docile species.