Chiming in late but:
The SoDak's were probably the best of the "treaty" BB's, although to be honest they probably broke the tonnage limit.
The only "new" BB's to go toe-to-to with comparable IJN ships were South Dakota and Washington at the 2nd Naval Battle of Guadalcanal. SoDak had her radar and superstructure damaged early in the battle and was unable to fire effectively, but Washington (a North Carolina class BB) made hash out of Kirishima in 7 minutes.
Interestingly enough, California, Tennessee and West Virgina were all extensively refitted, to the point where they kind of resembled the new battleships and were just as capable in terms of fire control (radar upgrades) and AA defense.
US BB's currently preserved:
New Jersey
Missouri
Wisconsin
Massachusetts
Alabama
North Carolina
Texas (the only WWI era BB preserved in the world).
Iowa is on donation hold, but she is in such poor condition (wooden teak decks are ruined for example) that it's going to cost a lot to preserve her.
A bit of preservation history:
Texas was the first BB preserved. She was donated to the state and a commission was set up to provide for her. The commission made some bad mistakes during the process and the ship was in terrible condition when she was turned over to the Texas Parks and Wildlife, which raised the funds have her drydocked and repaired. Currently a project is underway to dry berth the ship, thereby protecting the hull from continuous contact with sea water.
The next major preservation effort was in the late 1950's for the USS Enterprise, and it failed, consigning the greatest warship in US history to the scrap heap. The late 50's saw the scrapping of the last of the old battleships on the rolls.
Many of the preserved BB's have shown up in films. Texas and Missouri appeared in "Pearl Harbor", Alabama in "Under Siege" (subbing for the Missouri.)
