Hibernate is an Object-Relational Mapper. So are Entity Beans. Entity Beans are a part of the J2EE spec -- Hibernate is not.
The EJB3 spec has been greatly influenced by the success of Hibernate (
http://www.theserverside.com/news/thread.tss?thread_id=33450), but the two are not the same (regardless of how JBoss implements it under the covers).
The conclusion we came to in the book: EJB 2.1 CMP Entity Beans have fallen out of favor. Hibernate is catching a lot of buzz, but it is not spec-compliant. (We used it anyway.) EJB3 looks very interesting, but it won't be in mainstream use for another year or so.