The best thing about Polymer is that, unlike React, it works with W3C standards instead of going off on a tangent and hacking the DOM entirely. It extends current HTML5 standards instead of creating its own universe.
With Polymer, each component has its own mini-DOM which is actually a real DOM - Not the virtual layer you get in React which keeps overwriting the real DOM.
Unlike Angular, Polymer gives you a lot of control when it comes to how data flows throughout your app. Because of this, there are a few different component-level configs that you need get your head around. For example, by default in Polymer, data only flows downwards to child components, you have to enable a special 'notify' attribute to allow data to flow upwards to parents (this is different from Angular where data flows freely wherever there is a placeholder for it in your DOM).
I think React has been getting way too much hype. Polymer, on the other hand, is ridiculously under-hyped. Of those people I know who used both React and Polymer, all of them preferred Polymer. I'd like to hear alternative opinions from other people though.