I have recently stayed at each. I did get a nice room upgrade at the JW but in 3 stays in the past 12 months at the Ritz I have recieved no upgrades nor recognition for my Platnium status. That said the Ritz is a very nice property and the rooms upheld the Ritz standard. The are located within a couple of blocks of each other so location and my overall experience was a wash. If you are looking for upgrade and CL access i would recommend the JW.
If you want to save some points, I highly recommend the Renaisance Arts Hotel. It's a great boutique hotel with character. I was given an upgrade to a huge suite, and it's got a nice pool on the roof. It also has a nice contemperary design and a great French restaurant. Short walking distance to French Quarter.