The lack of a centralized Islamic authority, such as a Pope, is what makes dealing with Muslims so difficult. For Muslims, it is their religious books, and adherence to those books, that proscribe their lives and relation to a mosque and local religous leader.
There existed in the past powerful Muslim religous leaders located in large metropolitan centers such as Damascus, Cairo, Istanbul, or other Islamic cities, who would often go to war against one another in order to gain hegemony as ‘the most powerful Muslim spiritual leader’. Damascus held that position for a long time, even controlling events as far away in Spain for a long while.
Competition between these religous leaders was tough, but there has never been one official central encompassing religous leader for all of Islam world-wide. There is a group in Medina that is respected world-wide for its authority concerning Islamic law, and it has the final say on that subject. But Islam stretches from Morroco on the western shores of Africa all the way to New Guinea in the south Pacific and what sets it apart is that it is really so decentralized.
The Roman Catholic Pope, on the other hand, is in direct control of the Roman Catholic Church everywhere it exists: all priests, all nuns, all religous orders and over all laity.
There is no comparison.