Agree with Robbie.
Both received great reviews…so seeing the one that has been around longer might be advisable...before it closes. OTT has been open for a while now, and with the more recent opening and raves that AAiP has received, it seems that it will be around a while.
I saw both, and IMO you wouldn't go wrong with either one.
I saw OTT my first vacation night in NY and thought it was a sentimental way to start my return to New York!
OTT can be considered a bit dated. But then again, so is An American in Paris.
OTT comes off as carefree and fun (sailors on leave); Paris is more pensive and artistic, with lots of ballet-style dance.
The sets for Paris are very creative and lush. OTT is more cartoon-like and colorful.
Music for OTT is lighthearted, sometimes comical, and fun. For Paris…well…it's Gershwin. What can you say!
Both these shows are just great.