Yep, the numbers are going to vary for your family depending on whether you're staying value, mod or deluxe, how many people you have in one room, and what your eating habits are.
In general the
free dining plan is a bigger saver at the mods. AAA discount room only may save more money at the deluxes unless you have a bunch in one room and they are huge eaters. lol.
Values only have the quick service dining plan. So the room only discount often doesn't amount to much, but for some people the CS plan doesn't do the trick since you have no table service meals included.
Basically you need to crunch the realistic numbers about how you would eat on your trip (or how you COULD eat if you were trying to accomplish a certain goal), and get a quote on a AAA discount for your dates.
By how you "could" eat, what I mean is: If we (family of 5) were on a tight budget, we could-and have- done almost all CS meals, splitting meals even periodically. That allowed us to have a nice TS meal here and there without breaking the bank. Kept the food budget manageable. If that is an acceptable meal plan... that makes a room only discount a better deal.
When we want to have a sit down

meal every night and not worry about the price or budget, we are better booking the free dining plan an getting everyone in one room. Hard to do with 5, without going to a deluxe, which then blows the budget anyway.
Count the mouths you are feeding and price out your ideas.