The Byzantine Empire was definitely much more religion oriented than the Western Empire as it became a sort of hub of Christianity and then Islam. Politically it was much more stable compared to the Western Empire as it soon collapsed but the Byzantine Empire was able to prevail well into the medieval ages.
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.