AW and performance
I would expect this is mentioned elsewhere, but AW doesn't directly relate to cleaning performance- it is a measure of pure suction, which is only of relevance for what you feel when you put your hand over the hose.
Flowrate with the tools on the floor is key for pickup (and is rarely quoted!).
There was a recent legal case that Gtech won against dyson where the ruling mentions that dyson's adverts imply AW and pickup are directly linked, and that it's misleading.