What exactly do you want to ask with the question?
The main difference between AngularJS and ExtJS in my opinion is, that AngularJS focuses mainly on being a MVC Framework, which doesn't offer any extended library-style functionality to design fancy user interfaces. ExtJS goes a step further, it also is a MVC framework at the core, but offers more than that lots of functionality, for example designing of a user interface (probably what you mean by "Desktop Environment" lookalike). Visit the sencha homepage to get a full overview of the built in functionality. Using ExtJS to build webapp, there shouldn't be much of a need to add any other libraries.
To answer your second question: I don't think that ExtJS becomes deprecated, it has an active development and this year version 5 of the framework was launched.
The question "Should I use AngularJS or ExtJS" depends on the style of the frameworks, whatever you prefer and on your requirements. There are lots of articles which you may view, they compare the two frameworks in a detailed way: http://www.techferry.com/articles/ExtJS-vs-AngularJS.html
If you want to create an application with an user interface that looks like a Desktop Environment, you could either user ExtJS or AngularJS + a library, which provides functionality to create such an user interface.