Do you prefer this to Scrivener, or is it just better suited to some types of writing? Are you using the iPad app that syncs with this too?
No, to me there's no markdown app that competes with Scrivener. When I write in Scrivener, I often import lots of images and pdfs (which contain research articles, my data, outlines, mind maps and so on) into the research section, and then I use the split view to consult them side by side as I write my articles. Sometimes my papers also includes tables, which are much better dealt with in rich text format.
I have, however, taken to re-writing parts of my papers in 'minimalist' writing apps, mostly Byword and Simplenote, sometimes iaWriter. When I'm working on hashing out a particular idea or argument, I sometimes like to isolate it in a completely distraction free environment. I also use those apps for blogging, or for other kinds of writing where the final output isn't that long (say, up to five pages).
What I really like about Simplenote is that it provides a side pane where you see all your different notes (much as you do in a Scrivener project), so that it's easy to switch between them. I really like this in Ulysses as well - while I think iaWriter and Byword are great writing environments, I don't really like the fact that each document has to be stored as a separate file. Simplenote doesn't offer markdown, though, so one of the things that attracts me about Ulysses is the quite advanced feature set in terms of formatting, export and so on, combined with excellent organisation capacities (much enhanced version of Simplenote's side pane) and the ability to revert to a full screen 'minimalist' layout (in Simplenote, you can't get rid of the list of notes shown in the left hand side pane). But yes, Ulysses is expensive - but at least they're actually delivering quite a lot for that money - it's a much more advanced app than iaWriter or Byword.
I've had the iPad app, Deadalus, for quite some time. In the beginning I really liked it and used it a fair bit for note taking, but then moved over to Evernote and Simplenote due to cross platform/ iOS sync. I'd had Deadalus synced via Dropbox prior to that, but it made sense to use something that was fully coordinated across devices. I haven't used it much over the past year so can't comment much on what it's like at the moment. It organises your notes in stacks, which a lot of people seem to like. I prefer it to the each-document-one-file principle, but the Simplenote way of doing it is my favourite, I think.
Ulyssess III has a free demo version, if you want to check it out.