What is the difference between Polymer elements and AngularJS directives?

Question

On the Polymer Getting Started page, we see an example of Polymer in action:

Answer 1

1 & 2) Polymer components are scoped because of their hidden tree in the shadow dom. That means that their style and behaviour cannot bleed out. Angular is not scoped to that particular directive you create like a polymer web component. An angular directive could possibly conflict with something in your global scope. IMO the benefit you will get from polymer is what I explained.. modular components that have scoped css & JavaScript to that particular component that nothing can touch. Untouchable DOM!

Angular directives can be created so that you can annotate an element with several pieces of functionality. In Polymer web components that is not the case. If you want to combine functionality of components you include two components into another component (or wrap them in another component) or you can extend an existing component. Remember the main difference still is that each component is scoped in polymer web components. You can share css & js files across several components or you can inline them.

3) Yes, Angular plans on incorporating polymer in version 2+ according to Rob Dodson and Eric Bidelman

It's funny how nobody here has mentioned the word scope. I think that is one of the major differences.

There are many differences, but they also have a heck of a lot in common when it comes to creating modular lego like pieces of functionality for an app. I think it's safe to say that Angular would be the application framework and polymer could one day live in the same app along side directives with the major difference being scope but polymer may be a replacement for a lot of your current directives. But I see no reason why Angular could not work as-is and include polymer components as well.

Reading through the answers again while I write this, I noticed that Eric Bidelman(ebidel) did kind of cover that in his answer:

"Shadow DOM allows composing bits of HTML but also is a tool for encapsulating that HTML."

To give credit where credit is due, I got my answers from listening to many interviews with Rob Dodson and Eric Bidelman. But I feel the answer wasn't worded to give this guy's question the understanding that he wanted. With that said, I think I have touched on the answer he is looking for, but in no way do I possess more information about the subject than Rob Dodson and Eric Bidelman

Here are my main sources for the information I have gathered.

JavaScript Jabber - Polymer with Rob Dodson and Eric Bidelman

Shop Talk Show - Web Components With Rob Dodson