Benedict XVI eschewed the title because he wanted to emphasize the universal supremacy of the Bishop of Rome.  Eastern Orthodox patriarchs accept that the Bishop of Rome is also Patriarch of Rome and has ceremonial presidence before all other patriarchs (first among equals), but has no real power outside his particular Church (the Roman Catholic Church).  They would also agree that the Patriarch of Rome is the most influential due to the size of the RCC with 1.2 billion members.