Generally speaking, you'd use Angular with a backend framework.
Angular and other front-end frameworks are great for responding to user interactions extremely quickly, because often you don't have to go back to the server. And in addition when it does need to interact with the server, it is often faster to respond because it doesn't need to fetch anything but JSON data.
But that data needs to come from somewhere. And that's where Rails/Django/Play/Symphony/whatever are used.
AngularJS is a javascript front-end framework, it has little to do with the server, you still need Rails,Django,Spring or whatever to manage your server-side application.
It's not "this or that". AngularJS is a complementary framework for client side instead of server side.
That said, AngularJS can offload a lot of server side work. Mainly rendering views and the overall presentation layer. You can basically ditch your server side templating system and make your Rails, Django, PHP or node.js a simple REST API endpoint (with some additional auth system based on cookies or smth).
I realize this thread has me walking into the AngularJS den, but it is something i've been passively curious about.