[Firebase founder here] We talk about this briefly in our FAQ [1]. Here's the quote:
"PubNub and Pusher are both great services that provide simple real-time messaging for applications with a “publish / subscribe” model. Firebase takes a broader approach and provides real-time updates, data synchronization, and data persistence as one unified service.
This unified approach allows for simpler application development. Developers who build their software with Firebase will automatically handle real-time updates, and their products will work in “off-line mode”, both without any extra work from the developer. More importantly, Firebase can serve as a complete backend for most applications—completely eliminating the need for developers to manage servers and write server code."