Finagle looks like it is a bit lower level framework compared to vert.x. While Finagle aims to be a framework that supports services using multiple protocols, vert.x appears to be much more tailored for HTTP web services.
But take a look at the Finagle example from Heroku and compare it to the example from vert.x. There's a lot of boilerplate in the Finagle version because Finagle is a general purpose async service framework, which was my entire point.