Should I use @EJB or @Inject

The @EJB is used to inject EJB's only and is available for quite some time now. @Inject can inject any managed bean and is a part of the new CDI specification (since Java EE 6).

In simple cases you can simply change @EJB to @Inject. In more advanced cases (e.g. when you heavily depend on @EJB's attributes like beanName, lookup or beanInterface) than in order to use @Inject you would need to define a @Producer field or method.

These resources might be helpful to understand the differences between @EJB and @Produces and how to get the best of them:

Antonio Goncalves' blog:
CDI Part I
CDI Part II
CDI Part III

JBoss Weld documentation:
CDI and the Java EE ecosystem

StackOverflow:
Inject @EJB bean based on conditions

Update: This answer may be incorrect or out of date. Please see comments for details.

I switched from @Inject to @EJB because @EJB allows circular injection whereas @Inject pukes on it.

Details: I needed @PostConstruct to call an @Asynchronous method but it would do so synchronously. The only way to make the asynchronous call was to have the original call a method of another bean and have it call back the method of the original bean. To do this each bean needed a reference to the other -- thus circular. @Inject failed for this task whereas @EJB worked.

@Inject can inject any bean, while @EJB can only inject EJBs. You can use either to inject EJBs, but I'd prefer @Inject everywhere.