The primary difference is that Polymer is using built-in standards to provide their component lifecycle and style scoping. For instance, a React component has lifecycle methods like "componentWillMount" and a Polymer component has "connectedCallback". React will need to ship additional code to make their component model, and those lifecycle callbacks work. Polymer, gets all of that for free because Custom Elements are built into the browser (developer.mozilla.org/en-US/docs/Web/Web_Componen….
My advice for choosing any framework or library is to read the docs and see which one you prefer working with. Whatever makes you feel the most productive is the right one to use :)