If you wish to make a career in Europe, you better do the "JAR" training. The "FAA" training is directed for people living in the USA. Both have advantages and inconveniences. Doing one type of training, then converting into the other, is rather complicated and is somewhat expensive, particularly for holders of FAA certificates seeking JAR certification.
There is a little bit more to it then that.
Under FAA the "frozen" ATPL does not exist.
Converting from from FAA CPL to JAA fATPL is straightforward, 14 written exams passed and training as required for the practical. Been covered here many times.