Have you looked at Orgzly, and if so why didn't you go for it? I'm asking because I'm considering switching to Org mode for notes and looking for a good android client.
The main difference seems to be that Orgzly is a native Android app, while Organice is a (self-hosted) web service that happens to render nicely in a mobile browser.
I didn't to run a a whole separate server just so I could edit my org-mode files from a phone, so I like Orgzly better. But YMMV.
Lately I am trying to migrate to just running the native emacs on my phone with Termux :>
You're right that Orgzly is a native app, but you're spot on in that organice just happens to render nicely in a mobile browser. You also don't have to run a 'whole separate server' to use it.
I think writing/updating org-mode notes from mobile just doesn't have the good UX that I'd want. (Not as mobile-friendly as other apps; and not as easy to use or as powerful on a mobile as on a computer because of the limited form-factor).
I don't use mobile frequently for updating notes or scheduling things; so I can live with using some other app (e.g. OneNote/Sticky Notes) for inputting things on my phone,
then refiling that on my computer into org-mode.
I think Orgzly supports a read-heavy usecase like that quite well, since you still get to use org-agenda, have hierarchical notes to view, etc.
http://www.orgzly.com/