I have seen arguments that German naval radar was actually on a par with US fire control radar as far as accuracy goes. Take Tirpitz instead of Bismarck if you want ships at the same date. However German radars tended to fail a bit more often and from what I've read they didn't have as many reduntant sets. The US doctrine of engaging in long range fire I think would be a critical factor especially if you consider any likely strategic situation. A US battleship enagening a German one in WWII wouldn't really have to worry about holding back enough ammo for a second engagement while a German battleship especially if it's on a raiding cruise couldn't afford to shoot up most of its ammo unless they were ready to return to port anyway. A long range engagement would also tend to offset Bismarck's rate of fire advantage while emphasizing the advantages of the US "super heavy" AP rounds. A knife fight could go either way pretty easily but in a long range engagment I think Iowa or for that matter any of the US fast battleships has the edge.