Mobile framework world is extremely competitive one. recently, jQuery library was a king (as a mobile core framework), but far from the best one.

Don’t get me wrong, jQuery is a great library if you want to maintain, manipulate, and control DOM elements, unfortunately, it lacks MVC architecture and jQuery Mobile is a best example why this is a failed approach.On the other hand, AngularJS can do everything that jQuery does and much more, like:

1. MVC pattern
2. data binding
3. forms validation
4. dependency injections
5. templates

Ionic and Onsen UI are AngularJS based mobile UI frameworks. AngularJS core (approach) makes them very similar; if you ever wrote such application your transition is going to be smooth and painless.

Ionic  

Beauty of Ionic framework is in its modern simplicity. Ionic has a more mature feature and CSS component set and out of the box. Injectable delegate services, representing the UI elements (directives) gives you more control over UI/UX interactions. The development community is (currently) very active and it's gaining traction.

• command like "ionic start myApp tabs" still don't available in onsenUI
• Material Design like "Cardboard" are available
• Native theming and features 

Onsen

Onsen UI walks a similar path but unique in its own way. Default theme is naturally flat and distinctively different then Ionic one, especially if you spend some time playing with it. First time I saw it I was disappointed a bit, you need to understand it was after I decided to switch from ionic framework. Onsen UI is responsive.

• simpler structure, easy to start
• couple with Monaca IDE, some of features are only available only if you use Monaca. Otherwise, you have to create things by yourself.

Unlike Ionic, (this may change in the future) Onsen UI provides different themes for provided platforms. It CSS core is built around the Topcoat library . It is an open source CSS library designed with speed in mind. Because it doesn’t contain any JavaScript, Topcoat was chosen as a perfect UI building block.

Conclusion

There’s nothing controversial or false here; both frameworks will deliver what they’re promising. Onsen UI is somewhat vague about Android 2.3 support; I’m talking about the claim that Onsen UI works with this specific Android version. Personally, they should state that some features will not work on such an old Android platform.