Bismarck could win against a US Fast Battleship if she gets close. Her guns in theory according to the data charts on Navweps could punch through the belt of an Iowa class, hell if anything. The armored deck arrangement that Iowa class has is very similar to the armored deck of HMS Hood granted it has STS steel but it's three separate armor decks of decreasing thickness, but if Bisko can get a deck penetration, her rounds ought to bore deep into the ship, probably not into the Citadel unless they get extremely lucky but deep enough to give her a seriously hard knock. But Bisko will still likely loose unless clever maneuvering is used.
Uh. Right. I'm at work, so I don't have the time to go into this, but here's a key difference.
Iowa's belt is inclined outwards. That's to optimize against high-angle long-range fire, which increases the effective thickness of the belt at range. (How much? To give an example, fire coming in at 45 degrees has to penetrate
24 inches of KCA.
Her armor decks are thicker than Hood's, and the first, sacrificial one is meant to trip the fuze of plunging AP bombs and shells.
To be blunt, Iowa is designed to take advantage of her ability to fight at long range, and her armor scheme reflects that. Bismarck's armor scheme is optimized for the close-in brawl, and she's slower than Iowa. Significantly. (Which is a
damn funny thing to be saying about a 30-knot battleship. But I digress.)
Iowa, therefore, will be dictating the terms of engagement, and will choose a range that benefits her, rather than benefiting Bismarck.