Java EE 7 allows you to create new endpoints very easily through annotations. However, I was wondering is having multiple endpoints one to handle each message type a good idea
The only valid answer here is the latter option - having multiple endpoints.
See WebSocket spec chaper 2.1.3:
The API limits the registration of MessageHandlers per Session to be one MessageHandler per native websocket message type. [WSC 2.1.3-1] In other words, the developer can only register at most one Mes- sageHandler for incoming text messages, one MessageHandler for incoming binary messages, and one MessageHandler for incoming pong messages. The websocket implementation must generate an error if this restriction is violated [WSC 2.1.3-2].
As for using or not using multiple TCP connections - AFAIK currently there will be new connection for every client and there is no easy way how you can force anything else. WebSocket multiplexing should solve it, but I don't think any WebSocket API implementation support it (I might be wrong..)
Just noticed an ambiguity on my question re: message types. When I say message types I meant different kinds of application messages not native message types such as "binary" or "text". As such I marked @PavelBucek answer as the accepted one.
However, I did try an experiment with Glassfish and having two end points. My suspicions were correct and that there is a TCP connection established per connected endpoint. This would cause more load on the server side if there is more than one websocket endpoint being used on a single page.
As such I concluded that there should be only one endpoint to handle the application messages provided that everything is a single native type.
This would mean that the application needs to do the dispatching rather than relying on some higher level API to do it for us.