Yamato vs. Iowa - who would have won?

Here's the thing - by the time Iowa and Yamato were in use, the USN was building complete air superiority while the IJN was killing their own best pilots and planes.  After the USN had a few years of beating up IJN ships, the IJN commanders were exhausted, low on trained men, aircraft and fuel.  The Yamato couldn't even kill all of Taffy 3, and you think she'd stand up against an Iowa with air superiority and all her modern escorts.  

I think were talking about a theoretical match up of  Iowa and Yamato,each at their best,with their best crews no other factors such as airpower or weather.

What would happen then? 

I think one on one in their ww2 prime, unless an Iowa got an early compromizing shot in the Yamato wins more often then not. I think the speed of Iowa, better rate of fire and her radar even things up a bit but probably wouldn't win the day in a slugfest that she didn't score hard and early in.

Such a matchup of an early 1943 Yamato against a single early 1944 Iowa would have brought a smile to the IJN. 

Bill