We've stayed at all 3 resorts.
WL was our least favorite, although that was heavily influenced by the horrible bus service we had during our stay. I know it's not always this way, but if they suspend boat service due to weather issues (cold weather or t-storms), it seems to be fairly common for them to forget to send more buses. We also had a lot of issues with early morning buses trying to make pre-park opening meals. We waited nearly 50 min one morning for a bus and had 25-35 min waits the rest of our mornings. While the common areas in the resort are nice, it was our least fave for room decor and we had a few standout less than magical CMs. The TS options onsite are also our least favorite of your 3 noted resorts. And this is personal preference, but I didn't love the room decor.
AKL was really nice. We had a bunk bed room, so it felt a bit more spacious. The rooms at WL and AKL are small as far deluxe resorts go. Technically, they are bigger than the mods, but many feel the mods are configured in a way that give you just as much usable space as WL and AKL. In any event, we liked that during online check in, we were giving savanna choices in our room request options even though we weren't booked in a savanna view room. Beyond that, the CMs at AKL were all great, we like the dining options at AKL, we had great bus service at AKL (with one little annoyance), and the resort is so well themed that you really feel like you've been transported to a far off destination. Maybe it's the lack of real animals at WL, but AKL does a much better job of providing a convincing theme. The little bus issue...while buses start running at 6:30am, AKL is a 6:45am resort...so we had no choice but to take a cab for a 7am ADR.
I'm mixed on the Poly, mainly because I would rather stay at the Contemporary. The room size is great and I definitely prefer the large rooms like this if we're traveling as a family. I don't love but also don't hate the room decor and you can pick building preferences at 60 day check in to help ensure you're where you want to be. The Poly is also a great choice if you're going to MK a lot and we never found it a long trip to Epcot. The walk to the TTC only takes a few minutes and maybe it was time of day, but we never found overly large crowds or long waits when getting a monorail. It was never more than 25 min door to door. On the way home, we preferred exiting Epcot through the IG and taking a BC bus to MK before the boat or resort loop to the Poly. Considering Disney says that buses run at least every 20 minutes (+ drive time)...what we experienced from the Poly was on par with travel time from AKL and far less than anything from WL since we also shared with Ft Wilderness during our stay at WL. Plus the monorail is still more fun than the bus...at least for us. Where the Poly really shines is access to MK area dining. Obviously, you have Kona and 'Ohana, but an early morning breakfast at GFC or popping back to freshen up for a dinner at Narcoosee's or Cali Grill were so much easier when staying at the Poly. Captain Cooks is also a decent qs, we like Tambu for drinks, there's now Trader Sam's and Pineapple Lanai is perfect for no lines for Dole Whips. The CMs were great during our stay as well.
Ultimately, if it were me and budget isn't issue...I think the Poly will offer the best all around experience. AKL would be my second choice.
