I can't really evaluate any of the other moderates, but I can highly praise French Quarter. It's smallish, quiet, and has an intimacy I haven't experienced anywhere else on WDW grounds. No matter what time of day, you'll never feel like you're just one of many visitors; there are rarely large groups of people converging near the entry point to the complex (compared to the frenzied nature - but still somehow enjoyable - at Pop in and around the lobby and patio near the exit of the food court and entry to the pool). While there is live music most nights, and it IS a bit off-putting at first because you are at the end of a long day, it becomes part of the experience, and a welcome one.
The rooms are clean and comfortable, and include little embellishments that are missing at the values, like upgraded furniture and fixtures, the fashionable subway tile in the bathroom, nicer carpet, and most importantly for this guy, a ceiling fan -- there's something about circulating air that puts me to sleep and keeps me comfortable.
The theming is wonderful, from the brick-lined streets, the horse-head hitching posts that line the streets, and the occasional horse drawn carriage clip-clopping down those very streets. The food court is smaller than at the values, but you'll want to sit outside for breakfast anyway, weather willing (we did every morning of our visit, in JUNE!). The choices are not quite as plentiful in the food court, but good enough, especially if you'll be eating most of your meals at the parks.
I love that you can take a boat to DTD; we did this to catch La Nouba (wonderful, by the way), and it was very convenient.
Even if you don't choose the French Quarter, I hope that you'll at least pay a visit to check it out for future visits. I never thought I'd say this, but I think I might be willing to spend the extra money to stay at FQ instead of returning to POP. Time and money will tell.
I don't think I'd enjoy Riverside as much because of it's huge nature. Most of FQ's buses are specifically for FQ, but a few of them (DTD, AK, BB, and sometimes HS) share, at times, with Riverside; you'll stop at the south depot, the north depot, the west depot, the west-south-west depot, the home depot, the office depot; it sometimes feels like they'll never run out of depots at Riverside.
I doubt you can go wrong, but if you like small, intimate, and quiet, FQ is for you!