They are trying to solve the same problem: gatekeepers to any mutable data that affects your DOM -- but they do it in pretty different ways: (1) under the hood, Blaze tracks the DOM changes and applies them directly whereas React diffs the resultant HTML and applies the difference. (2) Blaze uses declarative templates for injecting HTML; React requires HTML to be built using virtual DOM elements in javascript.
Here is one of the React core developers (Pete Hunt) on React integration with Meteor: http://www.youtube.com/watch?v=qqVbr_LaCIo (note this is before Blaze)
Regarding performance: https://groups.google.com/forum/#!topic/meteor-core/-px_AGhj...