Well, the Eastern church was under the thumb of the eastern emperor a lot more than the western part. The emperor had a lot more control over the naming of bishops/patriarchs, and he also managed to get his way in many of their later councils/synods. Also, the Greek speaking east was much more prone to theological/philosophical exploration, and they produced quite a few of the doctrinal conflicts that required further definition of the faith, particularly in Christology. The Latin speaking west generally had a more practical bent, and would have been content with the Nicene creed, or even previous creeds that were less narrow. At least that is what I have gathered from my Church History class thus far. The texts for the class are The Story of Christianity: Volumes I and II, by Justo L Gonzalez. I recommend them highly, they are a good introductory source that provides a solid overview of Church history.
The primacy of the Bishop of Rome in the west was something that developed over time due to tradition and circumstance. From very early times, the Bishop of Rome was recognized as an authority of the highest rank, along with the Bishops of Antioch, Byzantium (later Constantinople), Alexandria, and perhaps a few others. All of these were large, influential cities that could claim (rightly or not) Apostolic origin. Over time, the primacy of Peter amongst the Apostles gave rise to an increasing respect for the Bishop of Rome. Another factor was the power vacuum left in the west when the capital of the empire was moved east to Constantinople. Over time, the empire's deteriorating organization and power in the west left the church, whose leaders were often highly regarded by the people, to take an ever increasing role in government. Since Rome was the capitol city of the western empire, this might have also played a role in the increasing authority of the Bishops of Rome. The Bishops of Rome began taking a more authoritarian stance as the final word on orthodoxy largely due, among other reasons, to it being the largest major western city in the empire, and the ever increasing doctrinal controversies springing up in the east, and also as a counterbalance to the authority of the eastern emperor who had too much authority (in many people's eyes) over the church in the east.
That's the way I understand it so far... hope it helped.