They both came from the same root: the "one holy, catholic, apostolic church" that existed from the early days of Christianity suffered a schism in 1054, with one branch being the Eastern Orthodox Church and the other being the Roman Catholic Church. Neither one is older than the other; either they both date from the founding of Christianity, or they both date from the time of the schism. Naturally, each claims that they are the only "one holy, catholic, apostolic church" and that the other has no claim to the title.
The Anathema was given 1054 AD from the Patriarch of Constantinople, and the reasons were many that had grown over the years. But Basic ones were the infallibility of the Pope and the "Filioque". You will find many controversies in the Catholic Church and the Bible. Other issues are the Purgatory that does not exist anywhere in the Bible but was taken as a fact. Many other issues you can find here:
They were one, then the Orthodox split from what we now call the Roman Catholic Church. They left because they no longer submit to the authority of the Pope.
The Orthodox and Catholic Churches were one and the same until they separated from one another in 1054 mainly over the role of the Pope.
There are very few theological differences. The main difference is that the Orthodox Churches (http://www.newadvent.org/cathen/11329a.htm) use the Byzantine Rite (http://www.newadvent.org/cathen/04312d.htm) and the Catholic Church use the Roman or Latin Rite.
Another difference is the Filioque clause in the Nicene Creed, the original which the Orthodox follow is
"And in the Holy Spirit, the Lord, and giver of life, who proceeds from the Father."
And the Catholic revision is:
And in the Holy Spirit, the Lord, and giver of life, who proceeds from the Father and the Son."
http://en.wikipedia.org/wiki/Filioque
Pope John Paul II said of the Orthodox Churches in Orientale Lumen, "A particularly close link already binds us. We have almost everything in common."
For the entire document, see: http://www.vatican.va/holy_father/john_paul_ii/apost_letters/documents/hf_jp-ii_apl_02051995_orientale-lumen_en.html
They were one church for over 1000 years. The split over the role of the Pope and other "papal claims", and over a change to the Nicene Creed.
From the Orthodox viewpoint, Rome tried to assert lordship over the other ancient Christian patriarchates, an arrangement previously unknown. Each patriarchate was fully in charge of its own churches, with Rome recognized only as the "first among equals" in honor, as decided in ecumenical councils; Rome's authority was limited to its own area. And Rome insisted on the insertion of the foliage "and the Son" into the Creed, an unnecessary and perhaps damaging addition to the Creed of the united church that had stood for 600 years. It was not in the approved Creed, and never had been. Ample historical documentation shows that the foliage was first added in Spain.
From the Roman viewpoint, the Eastern churches rejected what it saw as its legitimate authority. Rome also insisted the foliage was a necessary element that the East *removed* from the Creed.