Why would you need convert an FAA PPL to a JAA PPL?
Well, you wouldn't if you didn't want to fly a non-US registered aircraft.
You can for example with a non-JAA ICAO License (e.g. an FAA one) fly a G reg aircraft in UK AIRSPACE. But you could not fly it in the airspace of another JAA member state. Nor can you fly it within the UK within CAS where compliance with IFR is required, nor can you fly it to give instruction in flying.
Details
here.
If you want to fly a G-Reg somewhere other than the UK you need a JAA license.
The original question was regarding the difference between a JAA license and a "JAA Compliant" license. The simple fact is that an ICAO license and a JAA license give you different privileges when operating an aircraft whose State of registration is different to the State of license issue.
Mike