Well, the Eastern Orthodox Churches have patriarchs, and the lead patriarch is the Patriarch of Constantinople, head of the Greek Orthodox Church (although he's in Turkey). The Bishop of Rome is also the Patriarch of Rome, and was "first among equals" among the patriarchs until the split in 1054.

Even though Catholic parishes had a large degree of local autonomy, it's nice to have some sort of Prime Minister for the worldwide organization. The Second Vatican Council spelled out the principles of subsidiarity (decisions made at the lowest appropriate level) and collegiality (decisions made by consensus of equal colleagues). Most modern communities of nuns adhere to these principles very well, and it works very well for them. The "boys" aren't as willing to give up turf and adhere to these principles.

The Orthodox churches seem to be quite collegial in their style of management; but from what I've seen, they appear to be very much a "men's club," perhaps even more so than the Romans.

-Joe-