What were some differences between Byzantine Christianity and Roman Catholic Christianity?

Eastern Orthodoxy differed from Roman Catholicism on several points:

1: Papal Authority. The Eastern Church, like most Protestants, does not accept that the Bishop of Rome as a ‘Pope’ with authority over all Christians.

2. Only the 7 Ecumenical Councils and the Bible have authority for the Eastern Church. The Roman Church adds a Magesterium consisting of subsequent councils (attended by only its own denomination) and various Papal Bulls.

3. Filioque (double procession of the Holy Ghost): The local Council of Toledo added this to the Nicene Creed, and that modified version is used by the Roman but not the Eastern Church.

4. The Eastern Church uses leavened and the Roman unleavened bread for the Eucharist,

There are several other major liturgical and theological differences. Runciman has several excellent books about Byzantium which also cover religious topics.