A lot of this “difference” has to do with the weight distribution of the rifle. The modern M16 and variants have their balance point forward of the pistol grip. Thus, carrying muzzle down. With many of the WWII an earlier rifles, the balance point is closer to the grip due to the weight of the butt stock.
I have a vague sense of WWII pics and documentaries that you’d typically see M1 Garands carried muzzle up, but often see those with carbines carrying them muzzle down.