AngularJS was originally developed in 2009, is the oldest of the four frameworks. Due to this, it has largest community and has largest number of contributors. It is maintained by Google and a community of individual developers.
The AngularJS implements the MVC pattern to separate presentation, data, and logic components. Using dependency injection, Angular brings traditionally server-side services, such as view-dependent controllers, to client-side web applications. Consequently, much of the burden on the server can be reduced. That’s why you can see many news sites that using AngularJS on their front pages, like the Guardian, the Huffington Post, and MSNBC.
Becuase of its lightweight and very small download size compared to other frameworks, much popular application uses the Backbone framework including Twitter, Foursquare, Digg, Hulu, and LinkedIn Mobile. Also many music apps developed using Backbone like Soundcloud, Pitchfork, Pandora and more.
Knockout was developed and is maintained as an open source project by Steve Sanderson, a Microsoft employee. It is initially released in 2010. The framework has great documentation and includes features like declarative bindings, automatic UI refresh, dependency tracking and templating. The popular website build using KnockoutJS are jsfiddle, amctheatres, amctheatres, amctheatres and komplett.
KnockoutJS is better suited for smaller projects. You can also build very large, complex, and well structured applications. But you have to provide all of the structure beyond data binding and models.
Ember is also a very lightweight and fast loading. This is reason, many well known web applications adopted Ember like LivingSocial, Groupon, Zendesk, Discourse, and Square. Ember creators Tom Dale and Yehuda Katz say it’s easy to see when a site is using Ember because of its loading speed.
So if you’re only trying to create small widget or single page app, it might be overkill for you. It is awesome if you’re developing multipage, navigational, long-term projects.