Either, both, neither... it all depends on your particular Asperger's style.
Personally, I prefer that everything be in place - whether that means cleanliness, neatness, tidiness, organization, however you want to define it. I very much dislike chaos.
However, when I was younger, I absolutely loved neatness - putting everything in categories, lining things up neatly, sorting things and putting them in order, straightening out small things like drawers or countertops - but I couldn't stand to clean (and by this, I mean large things like an entire room). My whole room could be covered in papers, and I would spend hours sitting in the middle of it meticulously sorting a desk tray.
I'm pretty sure that I just got overwhelmed by the magnitude of the task and the planning (well beyond me at the time) required to orchestrate such a cleaning, and so I defaulted to my tiny, controllable organizational tasks. Nowadays, I recognize that this still happens if I let things get away from me (I'm a graduate student, so don't always have time to take care of every household task immediately), but since I know how overwhelmed I get by clutter and things out of place, I neaten and clean everything as soon as humanly possible.