What do we mean when we say "Migrating the specification level of Java EE projects"? Does this actually entail an application rewrite?
Basically, Java EE specification is backward compatible, so I don't think it requires you to rewrite your application code.
I think it rather means that you're moving from e.g. J2EE 1.4 to Java EE 6, so that you application server will provide additional features which you can but doesn't have to use.
However, in time, it might be required or acceptable to rewrite some of your application code because it might be cleaner, more maintainable, easier to read, faster, smaller and so on.