I am no expert, but...
it depends on what you want to fly!
Are you talking about work?
With the JAA licence you CAN fly an N reg in europe. With IFR you can also fly IFR!
But as far as I know you can only fly private.
The conversion from JAA ATP to FAA is much more simple than vise versa, takes a bit of time but I know someone who has done it. The FAA were very good and fairly immediate but the CAA as usual took their time and therefore it was a patience job and on the phone to the CAA all the time telling them to get their
in gear!
Good luck.
ps if you know anyone in Europe looking for low time FAA pilots pleeeeeez PM me!
Cheers