What advantages does hibernate provide over entity beans? Are there any limitations to hibernate?

Can you be more specific? You mean EJB 2 entity beans or EJB 3 entities? Hibernate, as everything else, has limitations. But you usually cannot tell until you face them. For instance, it cannot eagerly fetch more than one bag in a single query as discussed in another topic.

As for EJB 2 entity beans, well, I believe can only tell that they suck and plain objects rule! But then again, it's just my opinion.