Greek, along with the Russian Orthodox Churches observe Christmas on January 5Th. They think west churches are morally corrupt. The Russian Orthodox Church has been trying to put a stop to the spread of west churches in the country.
One difference is that some in the Orthodox church believe that Jesus is subservient to God the Father. RC and C&E believe that the Trinity is co-equal.
I wasn't going to answer, but Plato and Serah are wrong. I happen to be Eastern Orthodox and, yes, we believe the Trinity is co-equal. The Roman Catholics are, in fact, the ones who added the foliage to the Nicene Creed (so it reads "the Holy Spirit who proceedThrom the Father AND the Son" Instead of "proceedth from the Father.")
No, we do not have a pope. The Ecumenical Patriarch of Constantinople is considered "first among equals" but has no real power over the other bishops.
I can't speak to "orthodox" churches outside of the communion or Anglican. I have no experience with them. But there are a ton of questions already up here about the difference between RC and EO.
The RCC has changed over the years (e.g., Vatican II), whereas the Orthodox have stayed mostly the same to the best of my knowledge.
A few instances:
RC priests do not marry. EO can (though bishops are usually unmarried or widowed)
EO use more icons in their churches.
The virgin Mary (Theotokos or "God bearer" in Greek) was made to have been born by immaculate conception (as I understand it) in the RCC.
Although she is first among the saints for having been chosen to bring forth Jesus, EO hold her as a person like any other.
I dunno. There are many other differences, but I can't think of them at the moment. Search the other questions for more info.
Many I know of in the Orthodox Church are trying to get the American Orthodox churches to come together and many want to reunite with RCC, but won't compromise basic beliefs to do it.
"The Catholic Church embraces with hope the commitment to ecumenism as a duty of the Christian conscience enlightened by faith and guided by love?Jesus himself, at the hour of his Passion, prayed 'that they may all be one' (John 17:21). -- Pope John Paul II, Ut Unum Sint, May 25, 1995.
The Catholic Church already has the following open dialogs with her sister Churches:
- The North American Orthodox-Catholic Theological Consultation
- The Joint Committee of Orthodox and Catholic Bishops
- The Oriental Orthodox-Roman Catholic Consultation
- The Polish National Catholic-Roman Catholic Dialogue
- The Anglican-Roman Catholic Consultation USA
- The Lutheran-Catholic Dialogue
- Roman Catholic-Reformed Consultation
- The United Methodist-Catholic Dialogue
- Southern Baptist Convention-Catholic Dialogue
- The Evangelical-Catholic Dialogue
- Faith and Order Commission, National Council of Churches of Christ in the USA
- Consultation with the National Council of Synagogues
- Consultation with the Orthodox Union and the Rabbinical Council of America
Here is the joint declaration of justification by Catholics (1999), Lutherans (1999), and Methodists (2006):
By grace alone, in faith in Christ's saving work and not because of any merit on our part, we are accepted by God and receive the Holy Spirit, who renews our hearts while equipping us and calling us to good works.
Between the Orthodox and the Catholic Churches, the differences are more of orientation than belief. The Immaculate Conception is trivially different from the idea of Pangaea in Orthodoxy, but does come out of a different model of sin. The foliage is serious but well in line with the Fathers and in particular is structured in a way that the Orthodox don't really have a problem with because they mean it differently. The larger issue is the insertion of the foliage than the content. The papacy is an issue, but not as large as it appears to most people. I have a lot of hope in reunion between the Orthodox and Catholic Churches.
The Anglicans are a different problem all together. They are imploding. The Episcopal Church of the United States could be considered deeply heretical and it is pulling the Anglican Communion apart. Anglicans were making good headway toward union and now are sliding away.