In a nutshell, React encourages you to build applications with unidirectional flow and a mostly immutable style of data handling. React, however, mostly focuses this effort on the View. Cycle extends this encouragement to the entire application architecture and RxJS is its means of doing so in a consistent, reasonable way.

Pros to Cycle over React is that it is truly more "Reactive" in the best of ways, and in a way that is easier to work with (RxJS has a standard set of operators for building and composing reactive Observables that are shared with other platforms).

Cons to Cycle over React is that you lose "the Facebook effect". It's much more a project of love than of big enterprise and so it's a bit harder to learn and a bit more complicated at first glance. (That said, RxJS itself and all the Reactive Extensions libraries have gotten a lot of corporate love from companies as diverse as Microsoft and Netflix.)

http://reactivex.io is a great reference site to learn more about RX. http://cycle.js.org of course also has a very strong explanation of what is and how it expects to work.