I was recently evaluating the different frameworks for developing mobile web apps. I created an app in Sencha Touch, jQuery Mobile and JQTouch.(I also did a responsive web site using media queries, but this isn't so much a framework.) Here is my summary.
Sencha Touch is very different than anything I have used before. All of the content of the web app is built with JS. You code everything with JS. This causes things to be a bit janky, especially on older smart phones that need more time to process all that script. The biggest drawback, however, is that the online documentation is very difficult to use, especially for newbies. They have a few video tutorials online, but some are outdated and many are inconsistent (some use MVC architecture, for instance, which really throws you off if every other tutorial doesn't). All-in-all, if you are a web developer by trade and are used to manipulating DOM-level elements, this is a very frustrating framework to try to learn. Be ready to spend a serious amount of time on the learning curve. (Also, you have to pay Sencha if you want the latest and greatest version of their framework.) After attempting a few different projects with Sencha Touch over months, I grew frustrated and threw in the towel, even outsourcing the remainder of one project to India.
jQuery Mobile is well documented and has plenty of example code for you to follow along. You develop your web app as you would a website and use different data-xxxx attributes on HTML objects to describe how objects should be styled or used. Once you have your structure, jQuery Mobile takes care of the rest, making everything look nice and employing fancy animated screen transitions. There is a small learning curve when getting started, nothing compared to Sencha Touch. And last but not least, jQuery Mobile is FOSS and appears to be in very active development. I was very happy with the example projects I put together with jQuery Mobile. They were easy to finish and worked well.
JQTouch, when I evaluated it, didn't appear to be in active development. The documentation was a little sketch and I found the demo/example code and the documentation disagreed on how things should be implemented. It took some trial and error to find out which methods were correct. I wouldn't recommend this framework for development unless they have taken great strides in recent months.
In the end, no web app framework is perfect and completely replicates the native experience -- that hasn't happened, yet. With this said, I recommend jQuery Mobile and responsive web design as my favorites. They are different solutions for different problems (jQuery Mobile for a native-app experience, responsive for informational sites), but I would strongly suggest evaluating them if you have a new mobile web project coming up.