Apache CXF is an open source services framework. CXF helps you build and develop services using frontend programming APIs, like JAX-WS. These services can speak a variety of protocols such as SOAP, XML/HTTP, RESTful HTTP, or CORBA and work over a variety of transports such as HTTP, JMS or JBI.
Mule is the leading open source ESB (Enterprise Service Bus) and integration platform. It is a scalable, highly distributable object broker that can seamlessly handle interactions with services and applications using disparate transport and messaging technologies.