How did the political and religious ideas of the byzantine empire compare with the western empire?

the byzantine emperor was considered to be the highest political and religious figure. in the western empire, the highest political and religious figures were two different people.
the byzantine emperor was considered the political leader, but did not have authority over the church. in the western empire, the king had the highest political and religious authority.
the emperor of the byzantine empire was in favor of the use of religious icons, but the pope and bishops in the west were opposed, and excommunicated those who supported this.
the patriarch, as the religious authority in the byzantine empire, passed a law criminalizing iconoclasts, while the religious leaders in western empire supported iconoclasts and their religious ideas.