There are some doctrinal differences but they are minor. The major difference is in the rites. Roman Catholics use the Latin Rite while Orthodox Catholics use the Byzantine Rite.
Primarily, allegiance to the Pope, and the belief in the Orthodox church that the Holy Spirit proceeds from the Father, and not the Father and the Son.
Both believe in original sin, but differ on the way they explain how it is imputed.
All of the early Church Fathers are accepted by both. They believed in original sin. If an Eastern Orthodox says he does not, then he ignores his ancient Catholic roots.
The Eastern Orthodox were Catholic until some few centuries before protestantism. They are jealous of the Pope's location, and for that reason competed with him, though their Bishops are Successors to Bishops that earlier regarded the Pope as the first among the Hierarchy.
It is a matter of loyalty. I have noticed that Catholic Martyrs have always died with greater Peace than their Eastern Orthodox counterparts. I think that this is because they feel more spiritually settled in the House of GOD.