(okay, so the canned components are sometimes quite nice, whereas in vanilla Erlang you're on your own. The value something like Mule brings is more the abstractions and the ecosystem, even if the Java runtime is of no intrinsic help. Also, see RabbitMQ's slides on Erlang [2]. Mule isn't an outward-facing message middleware like RabbitMQ, but behaves a lot like one on the inside. It also gives canned components to interact with them.)
A Mule flow is often basically mid-level business logic plumbing; you don't want to put these flows on the public internet without rate limiting, authentication and authorization -- you want to use some API gateway or proxy in front. Mule has one, called Mule API Gateway, and the front-facing portal API Manager. Then the rest of the 'Anypoint' branded stuff is value-add: metrics, more connectors, SaaS stuff, etc. Overall, it's a pretty solid offering for when you need to do either lots of data munging or you gotta write APIs for a legacy backend; needs common in big orgs.
[1] http://www.enterpriseintegrationpatterns.com/patterns/messag...
[2] http://www.rabbitmq.com/resources/erlang-exchange-talk-final...