I think the kids will like ASM better and the parents Pop Century. Both are very nice and have very comparable accommodations. The difference is that ASM will have things the kids can relate to....Pop Century may not. But then again, Pop Century will be more fun for the adults and I feel the kids will enjoy them too. At Pop Century, you will have a chance to share parts of your childhood and memories with the kids. Being just 2 and 4 though, they may not appreciate your memories as much as living theirs.
No bad choice.........