Javascript performance on mobile Safari (iPad) is much more sensitive for my application that it is on the desktop. Some operations that work super-smooth on the desktop tak
If you have access to an Android phone, you can profile your application using desktop Chrome's developer tools and a USB cable (very convenient).
Android and iPhone behave+perform similarly, but not identically. That said, for 90% of use cases, if you improve performance on Android, you'll see the same improvements on iPhone.
Hour for hour, at least for the first pass of profiling, I think you'll get better results on iPhone using chrome+android to profile than using a less rich toolset.
https://developers.google.com/chrome/mobile/docs/debugging
It'll require Chrome, an Android device able to run the android Chrome app, and a USB cable.
You have to install and use the ADB console command, but once its working, you'll have the full chrome developer tools interface available for debugging mobile.
You could try using a javascript profiling library (using timers for example) by a bit of searching I've found http://remysharp.com/2007/04/20/performance-profiling-javascript/ but since I didn't test it I can't tell you if its any good. You could place timers at various locations in your code and try to track down the bottlenecks that way.
(Js Microtime Library http://phpjs.org/functions/microtime:472)