Yep, Within JAA land you can freely mix 'n match your license, medical, airframe, airspace, examiner, instructor and everything, since everybody has implemented the same basic set of regulations into their respective laws (JAR-FCL being the most relevant here).
There are some very minor implementation issues. UK not allowing VFR-on-top unless you hold an IMC or IR for instance. Netherlands recognising landings at night done as PICUS instead of PIC to qualify for the Night Qualification. And possibly a few more. One of these might be the reason to swap a JAA license from one issuing state to another. Or maybe some savings in P&P. But other than that, any JAA license is as good as any other.