The Ritz is in a much better location than the Windsor Court. Just off the Quarter, it's quiet but you can be in the action in three minutes if you so desire. Great bar with Jeremy Davenport on Thursday/Friday/Saturday nights.
However, the Ritz does not have a pool, the Windsor Court does. That alone might make it worthwhile to stay at the Windsor Court. It'll be hot and muggy when you're down there. Staying at the Ritz does allow you to use the pool at the Marriot, but that's a bit of a walk. The Roosevelt Hotel across the street from the Ritz does have a pool that you can purchase a pass for if you're not staying at the hotel.
If you do stay at the Ritz, the club floor is extremely nice and well run.