How did the Roman emperors differ from the Byzantine ones?

The Roman emperors ruled over a country stretching from the Atlantic to the Euphrates and from Britain to Africa. The Roman emperors were pagans, after death they were deified (often during their lifetime). They waged both offensive and defensive wars.
Byzantine emperors ruled over the eastern part of the empire. The western territories were not ruled by Byzantium for long. The emperors of Byzantium fought few wars of conquest, they basically had to defend themselves. Byzantine emperors hoped for diplomacy, pitting enemies against each other. They were Christians, considered anointed of God.