Recs.
Updated
SpecsUpdate
Pros
Pro Based on W3C's web components
Web Components are a collection of specifications released by W3C as a way to reduce the complexity of web apps by creating reusable components. Browser support is currently poor for web components, however Polymer is developed to make web components compatible with modern browsers.
Pro Seamless interoperability
As Polymer use the platform, always when it is possible, the web components built with Polymer are compatible with any other library, web-component, custom-element or framework. If you want to use a web-component you only have to import the web components spec polyfills (web-components-lite).
Pro Complete web app stack support
Full app stack from data tier to routing, progressive web app, responsive layouts makes no need to seek outside of Polymer ecosystem for application features.
In addition to waste set of mature web components in Polymer Elements along with Vaadin Elements there are thousands of web components in the wild comparable to jQuery plugins set.
Pro Based on web components
Web Components are a collection of specifications released by W3C as a way to reduce the complexity of web apps by creating reusable components. Browser support is currently poor for web components, however Polymer is developed to make web components compatible with modern browsers.
Cons
Con Compatible with only some of the latest browsers
Polymer is still very much in development and it yet doesn't support some older browsers. It doesn't even support IE 10.
Con Slow performance in mobile
Since most mobile web browsers don't have a very powerful JS engine, Polymer can be a little slow for mobile devices.
Recommendations
Comments
Out of Date Pros + Cons
Con No server side rendering
Polymer does not support server-side rendering. This results in higher loading times, more HTTP requests and it's not very SEO friendly, since search engines have no way of indexing a page if it's not rendered in the server.