While I can't say for certain, I just did three test battles using my models and the Micronauts rules set (which are pretty accurate if one mods them correctly). Three out of three times, the Bismarck was ripped to shreds by the Yamato. Reasons for this were manifold, but the decisive factors I found were this:
The Bismarck had 15 inch guns. 15 inch guns are relatively weak and completely outranged by the 18.1 inch found on the Yamato. All I had to do as Yamato was sit back and pound the Bismarck from long range, and there was nothing the German ship could do to reply because they weren't able to score penetrating hits on the Yamato's armor. The ONLY thing I could do for the Bismarck was go to flank speed and attempt to close the distance... HOWEVER... that had its own disadvantages. By closing distance, that made it easier for the Yamato to score more hits on the Bismarck, and getting hit up to SEVEN times with 18 inch shells hurts! It DOESN'T hurt so much getting hit up to seven times with 15 inch shells, particularly if they don't score penetrating hits on the armor.
In a mere three rounds I finished off the Bismarck at extremely close range. Keep in mind, 10,000 yards is considered point blank for 18 inch guns, whereas that's only "close" range for 15 inch. The best I was able to do with the Bismarck was knock out one of the Yamato's turrets and inflict some damage (not very crippling mind you) to her hull, as well as cause some flooding. Other than that I was cut to pieces every single time playing as the Bismarck against the Yamato, and the flooding I caused wasn't severe enough to sink the Japanese goliath.
The Yamato had a hull capable of withstanding a massive amount of damage as well. Pure attrition showed that the Bismarck was outclassed in this category too. I just simply wasn't able to withstand up to 20 hits by 18 inch guns. Likewise the Yamato was able to take the punishment of my 15 inch shell hits because I had to constantly try and close the range with Bismarck, which meant I wasn't able to penetrate her armor belt for a good chunk of the time I was doing so, inflicting only minimal damage on her.
So ultimately, I think Bismarck would need an insane amount of luck to survive an encounter with the Yamato. Of course, I was testing these conditions in broad daylight with no weather or darkness modifiers. At night there might be a better chance, but honestly, I'm not sure it would make much of a difference.
Granted this was with models and a rules set, albeit one that's mostly striving for accuracy, so I'm sure there are definitely variables you can throw in that a game just simply cannot duplicate for real life.
Also, this guy did a pretty good survey on which battleships outclassed each other, and details can be found here:
http://www.combinedfleet.com/baddest.htmand here :
http://www.combinedfleet.com/b_overal.htm Yamato clearly wins over Bismarck.
