The FAA licence is pretty much accepted everywhere in the world...except Europe, but remember that on the scheme of aviation Europe is but a pin prick on the globe!
Most of the Biz jets and some smaller privately owned aircraft in Europe are 'N' registered. Also the new Isle of Man aircraft register is the one to watch as they are dedicated to the biz jet end of the market, if the aircraft is registered as 'M-****' then the FAA or JAA licence is sufficient.
In the long run though it would be much easier to find work and keep work if you have both FAA and JAA tickets. Trust me, I've just found this out to my cost!