As with most other posters so far, I use both - although I visit A.org much more often, and post here more often - simply because people here know about the OS I use - OS3.9 .
If I had an Amigaone I would probably spend some more time over at AW.net, as the expertise in that OS is more concentrated over there (imho), however I don't own one.
Once I start using MOS more I'll probably spend a bit more time over at morphzone too.
I feel more at home in A.org, I don't know the etiquette, the history, the idiosyncracies of the people over at AW.net anywhere near as much.
Also, I find the interface and colour scheme of A.org more pleasing on the eyes - considering the amount of time I spend here that's an important factor.
Consider - go round to someone's house and start criticising them/their interests and they are likely to throw you out, or at least not invite you back. Same thing.
Also - try reading a few threads >40 posts over at aw.net and realise why people there are so pi55ed off by the same issues/criticisms/insults/comparisons - their site really does (and I am not blaming anyone here) seem to be quite plagued by flame fests, caused generally by (real or perceived) baiting, trolling, dragging up the past. It makes it really difficult to read any of the threads, and frankly if it was happening here as much I'd be a lot less inclined to spend time here. I sometimes think maybe there should be a "reply with an invitation to IRC to argue about it" button on AW.net.
This is not meant as any criticism of anyone, merely a comment on the state of affairs.