Whenever there's functionality you need that they don't use in their apps, it's not going to get developed by them, even if it's obvious it should be in the core. They always say to either submit a PR or create a separate module.
Onsen UI provides very clear, well-written and detailed documentation. It uses popular technologies that are likely already familiar to developers (such as jQuery and Angular). The framework is semantic and intuitive to use, making it quite fast to learn.
Ionic Framework is currently one of the most popular frameworks for hybrid mobile app development. This has resulted in a very large community of active users who contribute to the community by writing tutorials and answering questions.
Ionic is still a young framework (version 1.0 was released in May 2015). There are still some quirks and bugs in the framework to work out, which you can see a list of on their Github. However Ionic is under active development and bugs are generally addressed quickly.
jQuery Mobile works on any platform that supports HTML5. Cross-compatibility is a big focus for jQuery mobile, which includes developing with a progressive enhancement approach to support older browsers.
With the Level Editor components, you can let your players share their levels with the whole game community which is cool because you don't need to create new levels on your own, but the community helps you with it. There are other community features like rewards for good level creators that h...
Polymer apps are component based. You have to break down the layout of your UI into components, which makes it easier to understand how every part of the application works and how they relate with each other. This way it's also easier to maintain the application.
Web Components are a collection of specifications released by W3C as a way to reduce the complexity of web apps by creating reusable components. Browser support is currently poor for web components, however Polymer is developed to make web components compatible with modern browsers.
AppBuilder is a young project that's been fairly slow to gain popularity. This means the community is rather small, so there is a limited amount of 3rd party learning resources available. There is a forum, but it's not very active.
Sencha Touch is targeted towards enterprise-level development, and the price tag reflects that. There are many different product options available by Sencha. Most licenses start in the thousands of dollars, and require a minimum purchase of 5.