How did the histories of the Byzantine empire and Western Europe differ during era of the third wave civilizations?

Western Europe was msotly decntralised politclay which led to teh creation of local government and control of central authority in religious matters the pope was seen as leader and head of the Church, in the Byztaine emprie emperor was autcorat, system was cnetralised and emperor held supreme religious power over patriarchs it was known as cesaropapism, in western euorpe secular power and religious power were sperated concepts coined in augustinian philospohy