HI,
As far as I know the JAA and FAA don't recognise each other licences, even if both are ICAO licences. This is a real shame! I think this is more like an "political issue". It says in the JAR (JAA) that different states have to have some kind of agreement how to recognise each other licences and as far as I know JAA and FAA haven't been able to find this kind of agreement. I think that here in Europe we are afraid that all flight training should go to the US if we recognised FAA licences......
What comes to the recognision of CASA etc. I'm not sure. If you want to get some more details about JAA and conversion/licencing have a look in JAR-FCL 2.