I am a JAA/FAA/CAA pilot working in the United States. If you are young and motivated I would highly recommend to go and get your JAA licenses. It is indeed a painful process going through those 14 exams but I can say it is the best investment I have ever made. Those exams are not easy and you will need to study properly. Those are not "here baby, you will likely not pass on your own so here is the spoon feeding Gleim"
If you don't have experience to back up your FAA licenses, it surely opens a lot of doors on an international level.