I have stayed at both the Cabins and AoA suite. IMO, there is no comparison between the two. The cabins are absolutely gorgeous. And the area is remarkably relaxing. When you return to the cabins from the hotel, it is so serene it feels like another world from the busy resorts. It's hard to replicate that feeling in some of the larger resorts like the All Stars. As others have said, do not downplay the convenience of being able to park right at the cabin. For me, that is worth a lot; with our small kids, we are always carrying so much crap that loading and unloading is stressful and quite a chore. At the cabin, it's a breeze.
That said, I think with 6 you'll be tight in both. We've done 6 at both Cabins and AoA (our family of 4 + my parents) and it's tight. It's manageable, but it's tight. Honestly, I likely won't do that again. In the future, I'd likely request adjoining rooms or 2 cabins. But, it's doable-as long as everyone is on board.
Edit: be sure to take the family to the campfire. It's well done. Your older kids might not be interested, but I found the entertainer very funny.