It isn't so clear cut as Mikebatzel thinks. There are far more variables here at work than just a measure of the two ship's guns and armor. The conclusions in this link are worth digesting carefully on this type of engagement as a starter:

http://www.militaryhistoryonline.com...ceactions.aspx

I would think that given the performance of the two in actual operations that the Bismarck actually has a substancial advantage over the Yamato and would likely be the victor in a shoot out between the two.
Why? Because the Bismarck would have almost certainly put rounds on target within the first three salvos while Yamato would still be trying. The Yamato's fire control system.....note that system not just the rangefinders....is distinctly inferior in accuracy to that of Bismarck. This is why the Germans would almost certainly be first on target.
In getting on target first, the Yamato is likely to lose within the first 5 to 10 salvos:
* Primary fire control
* Coordinated command and control due to damage, particularly to the superstructure
* Any speed advantage
* Secondary armament
In addition, because the Japanese ship has a particularly bad internal layout (narrow passageways, small hatches, no systematic method of movement around the ship, lack of quick acting hatches etc) and poor damage control systems the damage suffered is going to go unchecked. This means systems lost or down due to damage are not going to get restored fully or partially.
Once the Yamato is degraded in performance, and if primary fire control is lost in particular, it is all over. Yamato hits nothing and loses the battle.