A key feature of AngularJS 2.0 is its support for Web Components [1]. Google’s Polymer is a Web Component polyfill (enabling them on all current browsers) and a framework on top of Web Components. This blog post describes how the Angular team sees the roles of AngularJS and Polymer.
AngularJS 2.0 team member Rob Eisenberg recently explained the relationship between AngularJS and Polymer:
Therefore, Eisenberg expects people to implement cross-framework UI components either as pure Web Components or via Polymer. He thinks apps and app-specific components are more likely to be built in Angular.
At Google I/O 2014, Google presented Paper Elements, custom elements following the new Material Design. These elements are Web Components, implemented via Polymer. They are very useful for Angular, especially version 2.0 and don’t compete with it. That is, Polymer as a Web Component polyfill and platform for widgets benefits Angular. However, Polymer as a framework does compete with it in some ways. It’ll be interesting to see how that plays out in the future.