Having stayed in all three (ASMu suites, cabins, and AoA suites), I can say that bedding is similar in all three. The fold-out stuff at ASMu is quite comfortable (better than my fold-out sofa at home lol) and pretty much the same as the fold-out sofa at AoA. The Innovabed at AoA is basically the same as the murphy at the cabins.
I love the cabins. It's one of my favorite ways to stay on property, and I love the proximity to Magic Kingdom as well as the overall atmosphere of Fort Wilderness.
That being said, with teenagers/older kids and/or more than two adults, I totally recommend the ASMu suites over the cabins.
There are two bathrooms in the ASMu suite - the cabins only have the one - and there is a desk/mirror in the master bedroom of the suite that does well as a makeup vanity too. There is more storage - two closet areas, various shelves and drawers in the furniture, and a bunch of shelves in the kitchen area - than there is at the cabin. There are two TVs in both the ASMu and the cabin, but both of the ones in ASMu are full-size (27"), while the one in the bedroom at the cabin is smaller. Again with bedding, the ASMu is queen-double-twin-twin, with the queen in one room and the others on the living room side. At the cabins, it's double-bunk-bunk-double, with the double murphy in the living room and all of the rest in the (small) back bedroom. I have happily/comfortably slept on the bottom bunk in past trips, but I am about 5'5" and my feet were at the end of the bed, so anyone taller might not appreciate it as much. In the cabins, there is a full kitchen with pots and full-size fridge/freezer, while in the ASMu suites the "kitchen" is a small resort-room cooler fridge ("dorm" sized), a microwave, and a coffee pot. We rarely cook for ourselves when at WDW anyway, so it never really mattered to us, but if you're planning on meals in the room to cut costs while there, the ASMu is great for making oatmeal and coffee in the mornings, but not really suitable for cooking meals otherwise, unless you really like those little cups of spaghettios or soup (things that don't need refrigeration, since there isn't much space for that).
Bedding - it's similar across the three.
Other details - not so much.