I've never stayed at either, so I don't know anything about the rooms except their placing, but I've been to both better times.
The French Quarter has a better theme, it's a little more interesting, espeically if you like jazz music. The rooms are close together. However, your dining options are limited, there is really only one food court. It has a Mardi Gras theme, and it's pretty good there. The pool here is big and shady, but the slide is really small.
Riverside's rooms are more spacious, and besides a really, really, cool and big food court with lots of dining options, there's a fancier and nicer restaurant called Boatwright's Dining Hall. Also, the pool is a little better at Riverside; the slide is way longer and more fun and the pool is really nice. There's a little bar next to it. However, the theme here is a little more boring.
Personally, I suggest Riverside for your stay, but in a way it doesn't matter all that much because you can still visit them both no matter where you stay.
