Having stayed at both a value (ASSp) and a moderate (POR) this year my opinion is that there really isn't much of a difference.
IMHO, the only difference is that the moderates have nicer themeing outside and are really well landscaped. Truly, the grounds at POR are beautiful! The insides, other than not being as loud decoration wise, are the same; although mods do have a mini-fridge.
The beds felt the same, the towels were the same, small and threadbare. Also, with the exception of POFQ, the resorts are HUGE. I would never stay at a mod (maybe POFQ) again. It took about 10 min to get to the main building from our room (we were the furthest away in the mansion section, on the 2nd floor). It doesn't seem like a big deal, but in 95 degree heat, it is; especially if you're just going for a mug refill.
I told DH after our July trip to POR that I will never stay in a mod again. We'll either go deluxe or value. I simply don't see the advantages to mod. Luckily for me, DH gave in and we bought DVC that trip!
With kids, I'd stay at a value and spend the $400 on great souvenirs and character meals. If you're just sleeping there and won't be touring the grounds, I don't think there's much advantage to the mod. I know people talk about the pools too, at mods there are water slides. It's my bet that if the kids don't know they're missing out on them, they won't miss them

. If you don't care about the sports theme (I don't care for sports, but sucked it up), ASSp is usually cheaper than all the others, so maybe you can save a little more.
Ok, ending the book now.

Good luck with your decision!