We both think that application development is going to radically change in the future and we're both building products that promote a new way of developing apps. We're stoked about Meteor and see our products as very complementary.
One minor quibble.. I like to think of Meteor as an "application platform" rather than a framework, because we're trying to take on some problems that web frameworks don't always tackle, like packaging and deployment. Also, we don't require you to use a particular strategy for generating HTML. For example, it makes sense to use backbone.js with Meteor, if that's your thing. At the end of the day, Meteor is about how you make all of the pieces fit together in a distributed cloud application. (For better or worse, that's what websites have morphed into, when you think about all of the APIs and services they use.)
Firebase is a realtime database that you could use with Meteor. The database we use in the Meteor video is MongoDB with Meteor's 'mongo-livedata' package, which adds some realtime glue to Mongo. But there are many potential advantages to using a database that is designed from the ground up to be realtime, and we're very excited that the smart guys at Firebase are taking this on. We predicted that this would happen eventually, but we had no idea it would be so soon.
(If you don't like the word realtime, please s/realtime/reactive/)
I used to work at Asana, where I worked with Luna, which is Asana's inhouse framework and is a distributed FRP system very much like a future-alien-technology version of Flapjax.