Facebook has been using React in production since 2011. Polymer is a "developer preview", aside from the Material Design presentation, I haven't heard of anything public-facing that Google's actually done with it yet.
React is backwards compatible to IE8. Polymer? Not so much. Unless you live in that mythical world of evergreen browsers, Polymer is sort of just a really great demo.
http://facebook.github.io/react/docs/working-with-the-browse... http://www.polymer-project.org/resources/compatibility.html