Right off I would say the Yamato and Musashi would win. And think, thank God I was on a tin can and not a battle wagon. But I do think the armor belts and teak deck would allow the US ships to absorb serious punishment. I think it would come down to the admirals. Who would as Lord Nelson put it, " forget tactics, just go straight at 'em." or who would try to turn this into some game of Go. I wouldn't put money on the Americans, not without air support.
This made me think of Kamichu. The Yamato comes home. That felt really neat.
The army of general George S. Patton or the army of US Grant, using weapons common to those of Alexander the Great?