I've used both Polymer and Vue for a few projects, and Vue's single file component method, coupled with WebPack, is almost identical to writing an app with Polymer.

Except that Vue doesn't ship with all the Polyfill baggage that Polymer does. Polymer has came a long way, but it still feels slow on anything but Chrome.

Once the Web Component spec is finalized, and built into browsers, I think Polymer will be a great choice. Today though, I gotta give the nod to Vue.