Polymer Elements are know as scope because of they act as an hidden tree in their dom. That means you can't predict their style and dome. However Angular is not scoped to that particular directive you can create like a polymer web component. An angular directive could possibly conflict with something in your global scope.
As we use Polymer and by the structure it shows that it relies on the Web Components, and the web component which are only supported by new mobile device only, But in case of AngularJS tries to use the similar operations, and simpler functionality with its Directives

And the reason we use Angular Directive because when we use this to construct new variables we have multiple ways to explain it. In Polymer web components this is not possible. If you want to combine functionality of components you include two components into another component (or wrap them in another component), you can extend an existing component only. You can share css & js files across several components or you can inline them.

With the Angular it gives you to develop and deploy higher that can make communication between server and enables routing and many others.These are know as high- level services.
Polymer, on the other hand, doesn't provide these things except as separate web components from their core library. Instead, it focuses on allowing you to create rich, powerful, reusable web components, which could be used to build webapps like those which are built with Angular. In the future, the lines could be blurred further as frameworks like Angular may leverage Web Components.