Regarding a Java EE Web application which is going to be served by a full Java EE Application server e.g. GlassFish, which is the best ORM Solution?
What you asked is which API is better: EJB3 (JPA) or Hibernate? I said that because you are asking about EJB3 JPA (which is API only) and Hibernate (which is implementation and API). Thus, to compare apples to apples you need to compare APIs. You choose between standard (JPA) and more powerful proprietary API (Hibernate).
But by choosing JPA there is another choice to make: for its implementation. By choosing Hibernate for implementation you can basically discard your question since both JPA and Hibernate are available.
So your question would change: which JPA implementation should I choose (between Hibernate, EclipseLink, OpenJPA, DataNucleus, etc.)?...