It developed differently because it was far away and the Empire was separated into eastern and western halves. They spoke Greek as opposed to Latin. They were more into Greek culture as opposed to Roman. Christianity became the religion as opposed to Roman multi-deities. Eventually even the capitol of the empire was moved to Byzantium (Constantinople). Also, having Constantine rule helped strengthen the Greek way of culture. While Rome was now controlled by Germanic tribes, Byzantine was strong and was under one autocratic leader, it's architecture took somewhat of a middle eastern look (in some cases) and compared to the columns of Rome it became more rounded and based on Christianity. Its status was much higher than Rome's its leaders were
