Polymer is based on Web Components, which are an upcoming Standard. Web Component performance might depend on the use case, but personally I think (without testing it) that native stuff is usually really fast. As far as I know, Web Components render directly to the DOM, as they are just HTML.
Now for the interesting part: How does Polymer fare against React? The answer: You cannot compare them. They solve different problems. Facebook states that in their docs:
Trying to compare and contrast React with WebComponents inevitably results in specious conclusions, because the two libraries are built to solve different problems. WebComponents provide strong encapsulation for reusable components, while React provides a declarative library that keeps the DOM in sync with your data. The two goals are complementary; engineers can mix-and-match the technologies. As a developer, you are free to use React in your WebComponents, or to use WebComponents in React, or both.
So it is really not against each other, but a completely different focus and they can be used together in one project, depending on your needs!