I finally got a chance to look up some specs here. Since we can tell from historical evidence that a combat of this sort would occur at 20,000 yards or less that both ship's main battery performance is such that the gun caliber really makes zero difference.
The German 15" at 20,000 yards penetrates about 19" of vertical plate, more than enough to go through any armor on the Yamato, while the angle of fall is about 13 degrees or, nearly flat. The 18" gun penetrates about 22" of armor vertically and is falling at about 10 degrees.
Therefore, it really does come down to who hits who first. My money is on the Germans.