Everyone is different but it wouldn't even be a question for us. We much prefer the POFQ to the All Star. Why?
The resort is much smaller. Only 1000 rooms. This makes the resort to "appear" less busy and not quite as crazy as it can get at the All Stars. The rooms are also a little bigger. Not much but a little. While we haven't stayed at All Stars, we did take a look at the room, and we noticed the difference. Many others may not.
We also prefer the "theme" of the FQ over All Stars. Again, a preference. We prefer the "greenery," the brick streets, the plants, fountains, alligators, jazz music, madigra theme in the food court area, the lounge at the pool and inside by the food court. And, they used to have live entertainment there. I'm not sure if they still do. We also like to walk down to Riverside and catch the lounge act there. Bob Jackson is wonderful and a very good family act. Hard to get a seat for him so you need to get there early or be ready to stand.
The boat to DTD is another draw for us. It is just a nice diversion. Plus, we enjoying being closer to DTD and Pleasure Island. This is especially true in the slow season since things close earlier except for these two places. Nice evening get away and it is close. They run both a boat to DTD and also one to Riverside. That is nice.
All in all, I think it comes down to what you prefer and what you are looking for in a resort. All of them are nice. I know I always look at staying at the deluxe resorts (especially YC) and every time when I compare the prices I keep going back to the moderate. So, I know exactly what is going on. Good luck with your decision. I'm sure you will have a great time wherever you stay.