The main benefits of Cycle.js in my eyes are:
1. Emphasis on a single entry point for event handling instead of a million separate event handlers. This is similar to the idea of the "Dispatcher" in Flux -- it's a central handler that manages all user input. But the Flux dispatcher has a specific purpose, whereas the main Cycle handler is more generic (which is, in my opinion, preferable).
2. Use of reactive programming, which is an extremely powerful paradigm in asynchronous environments like the browser. It takes a while to wrap your head around reactive programming but once you do it's absolutely fantastic. The only concern I would have here is that Rx.js adds overhead that might be unnecessary in some cases. But then I guess you would just use a more lightweight framework., so it's not exactly a criticism of Cycle.