what language did the eastern empire use? what were the advantages of this language compared to the language of the western church?

People of eastern empire that includes Antioch, Alexandria, Jerusalem and Byzantium used to spoke Greek language. However in the west Latin was used.

When capital of empire was transferred to Byzantium, Germans started their invasions that put the Europe into dark ages. At that time linguistic differences, political and economic turmoil, geographical distances caused the estrangement of west from east. So the eastern people got the advantage of Greek language as most of the theology experts used and spoke Greek language. Their were only few Latin based theologies for western people in comparison with the eastern side that has numerous Greek theologies to rely on. In addition to that vocabulary of Greek language was as vast almost ten times of Latin vocabulary that results in the decline of Latin literature as there were more expressive and deeper writing available in Greek language.