The API doc says that BasicPropertyAccessor (through getter/setter) is the recommended strategy : why is it better than DirectPropertyAccessor (access fields directly) ?

DirectPropertyAccessor let me put some business logic in my setters (check correctness of attribute) that do not have to be checked when I retrieve objects from db.

Depends, sometimes you want to do stuff in your setters/getters that need to be done even when data comes from the db. Besides it is better for maintainability.

And what happens if my setter method throw an application specific exception ? Does hibernate encapsulate it inside an HibernateExcpetion ?

It probably depends, but I would say no.
For sure, your Exception must be runtime.
I don't think the JavaBean spec allow exception in getter/setter.

It will, the InvocationTargetException which wraps the exception the setter throws (from the reflection call) will be wrapped in a PropertyAccessException (subclass of HibernateException)