I would have to say that, after a hard fought battle, the Iowa Class would have been the victor.  It is true that the Yamato Class was much, much bigger boasting heaver armor, however her much admired, huge 18.1in main guns would have failed her, as they failed her in every other engagement the Yamato Class fought in.  The 18.1in guns mounted by the Yamato Class were huge, and had great range and destructive capability, but were hindered by horrendous fire control.  In a previous post someone wrote that the Yamato Class were ?proven in battle and the Iowa Class was not? which is true, but not true.  The Iowa Class did exactly what it was built to do- bombard shore defenses and provide superior AA cover for the capital ships- the aircraft carriers.  The Iowa Class never had a chance to prove themselves in a battleship vs battleship encounter, however neither did the Yamato Class.  In fact the only thing the Yamato Class ?proved? is that it could take a lot of damage and provide excellent target practice before being destroyed.  Lets compare them based on actual battles.  The USS Washington (a North Carolina Class ? 2 classes behind the Iowa Class) engaged the Japanese battleship Kirishima and blew her out of the water.  Now the Kirishima was not anywhere as powerful as the Yamato Class, howerver it gives us a good look at how a US battleship with 16 in rifles fought.  The Washington?s guns were not as powerful as the Iowa Class (45 cal compared to the 50 cal of the Iowa) and the Iowa?s fire control was more advanced as well- still the Washington in 7 minutes of battle fired 75 radar tracked rounds on target from her main guns- that is almost 11 16in shells a minute.  The Kirishima was litterly blowen away.  In contrast take a look at the ?mighty? Yamato in her only ship vs ship gun dual battle- the battle off Samar when the Yamato led a strong battle fleet against the tiny Taffy 3 battle fleet.  Yamato had 3 supporting battleships, 6 heavy cruisers, 2 light cruisers, and 11 destroyers vs Taffy 3?s 6 small unarmored jeep carriers (used for anti-submarine duty), and 7 unarmored destroyers and destroyer escorts.  Just one 18.1 shell from the Yamato would have sent any of Taffy 3?s ships to the bottom.  The airplanes of Taffy 3?s group were armed to deal with submarines and Japanese ground troops-not surface ships, and certainly not battleships- so they are negligable for being able to enflict serious damage durring the battle.  For over 2 hours this huge Japanese task force is unable to defeate Taffy 3 and withdraws, having lost 3 heavy cruisers destroyed, 3 more heavy cruisers damaged, 1 destroyer sunk and 1 more damaged (the Americans lost 2 jeep carriers, 2 destroyers and 1 destroyer escort).  In this battle where the Japanese forces far outmatched the Americans (on paper) where was the great Yamato?s huge artillery?  The Iowa Class would have beaten a Yamato Class in single combat due primarilly to supperior fire controll (Iowa) vs horrendous fire control (Yamato).  The Iowa Class could fire at flank speed with radar controlled precision, whereas the Yamato would have to plot every shot the old fashioned way.  The Yamato, with her superior armor, would have taken a lot of damage before going down- thus given the American crew great target pratice, but in the end huge artillery with no modern fire control is no match for proven, powerful artillery boasting modern fire control systems.  The Japanese simply lost the technology race for ranged artillery.