We didn't specifically look at appMobi, but as far as I know Titanium is the only (relatively mature) framework that compiles to native Obj C, and is not just a wrapper for HTML5. The performance difference is enormous.
To be honest I've only built games and in that sense appMobi has an edge with their DirectCanvas technlogy which speeds up the canvas rendering on mobile devices by 500% (according to them). I guess you don't use any canvas though so not really relevant in your case.
Thanks for the reply anyway. I will definitely have a closer look at Titanium.
If you're making cross-platform games, you may want to take a look at playn, we have been using it for over 5 months, and it has been really easy to use and works really good, though some platforms are still a work in progress http://code.google.com/p/playn