Intro
A larger version of this answer can also be found HERE.
jQuery Mobile was never intended to be used only as an HTML5/CSS3 hybrid mobile app framework. On a similar track like its older brother jQuery and jQuery UI it was intended to be used as a robust, responsive solution in the ever growing mobile web application market. What it took from its older brother was an all around browser support. Run it on every possible major platform and it should work just the same.
That same broad browser support also brought another problem and that is platform optimization. Because jQM can't favor specific platforms also means it is not optimized to use most in any of it.
Let us also talk about Phonegap a bit. While great app packaging system it becomes a hell hole when used with a larger jQuery Mobile application. It's like two great parents made a deformed bastard child or to large pluses gave as an even bigger minus.
Solutions
Like always in human history another groups of developers came to fill this evident hole. And here came jqMobi (now AppFramework), jqTouch, Zepto, Sencha Touch, Trigger.io and others.
Good vs ...
Before going any further than jQuery Mobile one thing must be understood, whatever you gain in speed (and trust me you will get it), you will lose in community support. While every earlier mentioned framework has a sizable developer community behind them, all of them combined can't even come close to jQM.
With this said, let us delve into specifics. From my experience currently two best solutions as HTML5/CSS3 Android and iOS hybrid app frameworks are AppFramework and Sencha Touch. First, let me say, they are fast, faster than jQuery Mobile will ever be (if jQ developers stay on this course). UI support is similar if not even better in the case of Sencha Touch, not to mention UI is more native looking that it is the case with jQuery Mobile. Listviews are faster, scrolling is better, transitions do not stutter.
... bad
Before someone asks why do people then choose to use, jQuery Mobile instead? The obvious reason would be community support and to some extent, this is the truth. But there are some other pressing matters here. While jQMoby advertise it self as a truer jQuery alternative to jQuery Mobile it is a big lie. While still a great an excellent framework they are using this saying as a marketing trick. They have indeed cloned (redone them) a lot of jQuery features but this is only a partial job, and veteran jQuery developers are going to find them self in a problem. They will not be able to make fully the most of their previous knowledge thus spending more time trying to find how to do something that was supposed to work than working on an app.
On the other hand Sencha Touch doesn't suffer from this problem because it has a different, almost alien syntax. Like with jqMoby you will need a lot of time to get into its syntax. But have no fear, the result will be satisfactory in the end.
One other thing, unlike jQuery Mobile and Phonegap, AppFramework and Sencha Touch has their native app packaging system. In my humble opinion, this system is better than Phonegap because they are made to work with their js frameworks. Only thing Phonegap have over them is a HUGE plugin development community.
Links
jQuery vs Zepto vs jQMobi - which one is the fastest?
In this case jQuery is like jQuery Mobile because test here relays on
an underlying framework functionality which jQM takes from jQ.
Good ranting on jQuery Mobile vs. Sencha Touch
Title says it all.
AppFramework forum
Only good jqMoby support site
Sencha Touch forum
Only good Sencha Touch support site
Conclusion
AppFramework is probably the best choice for you. It has a similar
design as jQuery Mobile so the syntax is not going to be a problem.