Which is more powerful the popes or the Patriarch. why?

The pope is first and foremost the bishop of Rome. As such, he has full authority over all aspects of the Diocese of Rome, just as any bishop does over his diocese. The pope today delegates his authority over the diocese of Rome to a vicar, presumably because he is too busy to worry about the actual needs of the faithful of Rome. Some popes, however, have taken a more active role in the pastoral care of Romans.