How does RabbitMQ compare to Mule

Mule is a "higher level" service implemented with message broker. From the docs

The messaging backbone of the ESB is usually implemented using JMS, but any other message server implementation could be used

You can build an ESB with rabbit; however, you're going to be limited to sending byte[] packages, and you'll have to build your system out of messaging primitives like topics and queues. It might be a bit faster (based on absolutely no benchmarking, testing or data) because there are fewer layers of translation. Mule provides an abstraction on top of this, speaks a variety of transports, and can handle some routing logic.

Mule is an ESB (Enterprise Service Bus). RabbitMQ is a message broker.

An ESB provides added layers atop of a message broker such as routing, transformations and business process management. It is a mediator between applications, integrating Web Services, REST endpoints, database connections, email and ftp servers - you name it. It is a high-level integration backbone which orchestrates interoperability within a network of applications that speak different protocols.

A message broker is a lower level component which enables you as a developer to relay raw messages between publishers and subscribers, typically between components of the same system but not always. It is used to enable asynchronous processing to keep response times low. Some tasks take longer to process and you don't want them to hold things up if they're not time-sensitive. Instead, post a message to a queue (as a publisher) and have a subscriber pick it up and process it "later".