They don't solve the same problem. ExtJS is a UI toolkit, AngularJS is more of an application framework - Angular doesn't provide complex controls, Ext doesn't provide a defined structure in which to build your code.
It did not provide simple controls either, no basic DropDown or DataGrid,ListBox.
It only made super easy to make Hellpo world apps with the 2-way data bindings and that is all, when things get complex angular can't also gets super complex.
Yes ExtJS could be thought of as a component/ui framework similar to Bootstrap or KendoUI?
Before Angular, Backbone was all the rage (2013) which started the whole front end framework trend and effectively killed jQuery (which was only really good for manipulating the DOM because JavaScript was so fragmented since not every browser supported the JS function... eg. IE6).
Essentially Angular wrapped everything into a nice gift that included Backbone-like MVC type architecture (MVVM), KnockoutJS, and Mustache for Templates (Similar to ERB for Rails?).
I'm definitely incorrect in the descriptions in the plumbing because it feels like ancient history now. Essentially Angular is just a framework like Rails for the Front End. Difference between ExtJS is that it's more heavily into the way the UI widgets worked and behaved whereas Angular is more for the Business Logic and the way the Client Side is structured.
Then IMO angular should have not do GUI part at all, rather then the bad thing they created in angular1.
Honestly I have no idea why would you compare angular with Rails, it includes some basic routing, and some pathetic wrappers for existing native functions, and the $emit/$on , what other plumbing I am forgetting ?
There are still a ton of super quality jQuery plugins for Widgets that are still used today, I seen a lot of angular code just wrapping (badly most of the time) jQuery. And on top of that angularjs used jQuery (or a lite version) too.
Did you wrote desktop or mobile application with the native toolkits ? I am curious if the misunderstandings are because if you only used Web tech then angular would appear to be something great where if you come from Desktop/Mobile you see angularjs as garbage, better then bad jQuery code but probably worse then anything else.
But at the time of Angular's release, ExtJS was already 3 years old.