Something I've been curious about is that top-down hierarchy probably gave the Western branch of Christianity as much of an advantage over the East as its geography did. If the styles of church governance had been reversed, for instance a first among equals ecclesiastical government in the Latin West and a top-down Greek East, how might that have changed things? To have the top-down hierarchy would require the Arab irruption to possibly change in nature from a new religion to perhaps one variation of Ethiopian Christianity, maybe? Regardless of how a Catholic system of governance evolves in the East and an Orthodox one in the West, what impact does this have on both branches and how might the variations of Christendom that emerged have ended up different?