Since you asked for opinions I'll put in mine too...
Assuming that the extra $$ will not impede your enjoyment, I vote for the Poly.
We've now stayed at all three all stars and at each of the deluxe and moderate resorts. I just need to book a few days at POP sometime to completely sleep my way around the world - wait that didn't sound too good... well, hopefully you know what I mean
Anyway, at the risk of sounding like a hotel snob (I'm not - really I swear - it's the kids & DH who are) I feel the magic much more at the Poly than at All Stars - from check-in to check-out. This might get long but let me give you a few reasons why...
At ASMu we enter the lobby, It's a busy place and a bit loud. If we've driven I need to park in one lot to check in then find another one closer to the room afterwards to leave the car in and haul the luggage from. When we've flown our luggage waited in the lobby with us after being unloaded from the bus.
I get in a line that's normally rather long, snaking thru the roped off areas giving me a feel for what busy park attractions will be like, while the rest of the family searches for seats among the huddled masses in a lobby filled with people and baggage.
After check-in if our room is ready, we wander aimlessly looking at building numbers and signs, often past large groups of loud high school kids staying there for festivals or competitions toting our luggage along like pack mules (Now don't get me wrong, I LIKE high school kids and pack mules though I wouldn't want to be either at my age. DD17 has been one of those chorus/dance/sports kids at ASMu. They have an awesome time and it makes me smile just to watch them but they tend to be loud, very active and Everywhere so not all family groups appreciate them as I do).
I have not found the front desk staff or food court CMs to be very warm & fuzzy although they do give out balloon animals or regular balloons to kids at check-in when they have them which is a nice touch.
The busses are often crowded during busy times, I may have to wait for a second or third bus to be able to find one with room for all of us, and there is only one bus stop so I try not to be in one of the furthest buildings because the walk back at night when we're all tired doesn't top my list of fun attractions.
The suites have a nice location within the resort but they also feature sleep sofas. I don't know about you but after a day or two, the novelty of the sleep sofa would wear off and our kids would be complaining that it wasn't as comfortable as a normal bed and why did they have to sleep there...
At the Poly, we enter the lobby past a soothing fish pond, are greeted with flower leis and Disney Adventures magazines for the kids, bell services takes our bags, if we've driven the valet guys happily take our van and return it when we ask with the a/c already on to cool it down.
I'm sure the front desk line can get busy but we've yet to personally experience a long line. There are benches amid the flowers and a comfy area with a tv on for the kids to wait in just in case though. Occassionally the CM in the lobby will be showing guests how to hula or make leis which is interesting as well.
If our room is ready we wander thru the resort in search of it but it's peaceful outside, the number of buildings is limited and bell services has our luggage to deliver for us so the room search is not that big a deal. The monorail, bus stop and boat docks are more centrally located making it seem like an easier commute to the parks & back at night. The beds are comfortable and the rooms have been remodeled in the past few years. Mousekeeping will make up the day bed each evening with turn down service so there's no complaints that it isn't a 'normal' bed.
Speaking of beds... will your youngest nap during the day? If so, that's a major plus for a deluxe hotel. The stroller is another issue that would sway me to a deluxe with proximity to several parks simply because of the hassle of folding/unfolding/carting the stroller while carrying a sleeping child on and off a crowded bus....
Whew... Now all that said, have you given any thought to my personal favorite the YC/BC? Typically the rates for the BC or YC are a bit less than the Poly so the difference in price would be less noticeable but you still have the space and convienent location along with more amenities.
Your children are different ages and the pool there is perfect for that. The area for small children is especially nice and very large with a sand bottom and lots of buckets and shovels to play with keeping them busy for hours - unlike the smaller concrete toddler pools of the value resorts.
With older children, you may spend more time in Epcot or MGM than in MK. The sidewalk and watertaxi to those parks is wonderful. You can rent boats for fun at the marina and family bikes at the Boardwalk. At night there are bonfires and movies on the beach.
The CMs are great. Art, the BC's geeter is truly magical and has a way of making even the smallest child feel listened to and appreciated. I've stayed lots of places but I have never felt more welcome anywhere...