Stress testing is fun and all other tests typically test your app with a single thread. However: once deployed, your application will never again run in a single threaded environment... So unit tests are nice, but stress tests are absolutely necessary in a Java EE environment.
My (Adam Bien) JavaOne talk: "Stress Testing JavaEE Applications" is available online:
On demand workshops: Java EE 7: Bootstrap, Effective, Testing and Microservices available for streaming.