Actually, all either ship has to do is get in one good salvo with several hits on the other and the one that hits first is almost certain to be the winner of the action. If you look at actual results from WW 2 of battleship on battleship actions the turret face armor is irrelevant. It is the roof armor and barbette armor that makes the biggest difference. In both ships they are vulnerable to strikes in these locations. The Bismarck is far less vulnerable to the diving shell. Her torpedo defense system is deeper and better arranged than that in Yamato. In particular, Yamato is very vulnerable to flooding due to having the only completely dry torpedo defense system on a battleship in WW 2. Belt hits are generally rare so this really makes little difference. Deck armor is what is important. Yamato uses a single thick deck (but not consistantly one thick plate in many places) versus the two deck system on Bismarck. Neither is going to completely protect the ship from heavy hits at long range regardless of the paper figures usually cited. Bismarck is far better in fire control than Yamato (assuming 1941 for both). The Germans had a predictor system very comparable to that in US or British battleships of the time using a three-axis mechanical computer tied to the rangefinders. The Japanese system is less complex and more comparable to those in use in the early 30's and lacks a true stable vertical element. In both battles Bismarck fought she was on target getting straddles before the British were. Only bad luck kept her from making any hits on Rodney before succumbing to British fire. In the one fight Yamato was in, Samar, her firing performance was relatively abyssimal struggling to get on target and slow to do so. This factor alone gives the German ship an enormous advantage over her Japanese opponet. If both had their radar as fitted neither gains any real advantage from it. Neither incorporated this system into their fire control. At best it could have only been used for ranging and as a manual input even then. Basically, I can't just give the battle to the Japanese on the basis of a couple of inches of gun caliber and somewhat heavier armor.