1) It's a pretty safe bet that your kids will love any place that has a pool. (And they all have pools.)
2) The pools at the moderates and deluxes have water slides. The deluxes (at least some of them, don't know about all) also have splash areas. (And hot tubs, which might be kinda important for the Old Folks.)
3) When you move from value to moderate, most of the beds go from double to queen sized, too. Might be important for the grownups.
4) Most of the values have a food court. When you move to moderates, they generally have actual restaurants. (Some people prefer the food court, cause they're heading to the park as soon as they can, anyway. Just letting you know the choices.)
5) Wilderness Lodge has rooms with bunk beds. Might be a real treat.
6) Wilderness Lodge is also just a boat ride from Magic Kingdom. And a (different) boat from the Fort Wilderness campground (which has the Hoop de Do Musical Revue, and Mickey's Backyard BBQ.), and from Contemporary (which has Chef Mickeys, an all you can eat buffet where you can watch the monorails drive through the building, and where Mickey and Donald and Goofy and friends will come to your table for photos and autographs.)
7) Yeah, AoA certainly has a lot of theming. (Lots of the values do.) but I will note that at AoA, you'll either be in a Little Mermaid room (Don't know how the boys feel about that), or you'll be paying more for a Family Suite with a Nemo, Cars, or Lion King theme. (You might want the suite, even though you only have four people. You'll get a mini kitchen, a dining table, and a queen sized bed in the separate master bedroom.)
8) Having said all that? It's your first trip. Odds are, you're not going to be spending much time at the resort. Maybe breakfast, and maybe a break for pool and/or nap in the afternoon.
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PS: just read the people who responded, while I was typing this. And I admit I don;t know much about the place, but I suspect that Pirate Rooms might make a big impression.