We stayed at French Quarter last November. We loved it! We loved that it was smaller then all the other resorts. It seemed less crowded and quieter. The pool and jacuzzi was never crowded but we were there in the beginning of November.
As far as transportation, it was great in the morning but crowded when the parks closed.
The best part of the resort is the Beignets! I ate lots of them lol.
I've stayed at both and loved both, and will probably always stay at one or the other. FQ might have a slight edge for me, but I don't think you could go wrong with either. FQ was a little quieter but I didn't feel like it was a big difference. I love that both hotels have a boat to Downtown Disney. Only Riverside has the "royal rooms".