(as with all my posts, please correct me where you think I'm wrong)
Podkarpatska reminded me of this.
In the west, the Church claimed the power (more so during the middle ages) over state governments in terns if being able to appoint and depose state leaders, as well as influence policy. In the east, it appears the "emperor" or other state governments were given some power over the Church.
If this is an accurate view, it seems that the west made it's position best favorable to the Church, to ensure less influence on outside (not clerical or spiritual) forces acting on Church policy and theology.