I would say that while the Eastern Orthodox churches have their own set of problems, - they more likely reflect the mission of the early fundamental 'true' church.
I'm Coptic Orthodox, a type of Orthodox. Coptic means Egyptian.
Well, Easterners believe that churches should have icons, but not statues. They also believe that during the liturgy, or mass, that the bread and wine become the Body and Blood of Christ--before it even goes into your mouth. The Catholics believe that its bread and wine, and then once it TOUCHES your mouth, it's the Body and Blood of Christ.
We are also VERY peaceful and tolerate. The Coptic Orthodox have a Pope, Pope Shenouda III, and the Greeks have a pope, too; but I don't know his name.
The Eastern Churches are also very different than the Catholic churches. You can go ogle that for photos.
The bigger question is why did the western church have such things? My personal feeling is that the western church became very political and was part of the first child to the property and 2ND child to the church and the 3rd child to the military or reverse of the last 2. So it was more family that religion to my thinking.
I think the big difference is the Nicean Code in which Constantine (worshiper of sun god) embraced Christianity or had them decide on their tenants and they did not agree. The western church felt that Rome was primary and predominant and the eastern church had each bishop to have authority for the area and did not recognize Rome as the ruling group. There were certain scriptures that were accepted and some that were rejected. They decided on a number of things that were in the early church that would not be part of their beliefs and some that were as part of the Nicean Code. There were disagreements as to what should and should not be accepted and led to the split.
I am an Eastern Orthodox christian- While the Church did not carry out things like a witch hunt or Inquisition
and were forbidden to kill people the governments execute people for heresy and blasphemy.
For example the so called old believers Also Justinian (r. 527-565) ordered death by fire, intestacy, and confiscation of all possessions by the State to be the punishment for heresy against the Christian faith in his Justinian code. these were the acts of the state not the church. Also look up Vlad III of Walachia.
It is clear that we are sinners to and need Christ. So I will not Denney we didn't do these things.
Also Eastern Europe in the time of the witch hunts tended to do vampire hunts- which involved staking dead bodies.
edit I am a convert and I converted because we kept the doctrines unchanged and did not canonize the works of Aristotle due to our concept of mystery.
Eastern Orthodoxy never had religious and political power in the hands of one man, such as occurred in the West in the Pope of Rome. Orthodoxy's "power structure" is distributed among various patriarchs and archbishops, with the Patriarch of Constantinople, AKA the Ecumenical Patriarch being "first among equals", but with a guiding and assisting role, not a ruling role. He may not interfere in the internal workings of any jurisdictions other than his own, though he may be invited from time to time to mediate between jurisdictions.
First, it must said that the Eastern Orthodox Church is comprised of a myriad of national Churches, each with it's own history and tradition. While they have much in common, it is not easy to generalize.
Your question focuses on the "dark chapters" in the history of Western Christianity. We hear more about these episodes simply because we live in the West. Eastern Orthodoxy, unfortunately, also has had some dark episodes in the past. Two immediately come to mind:
* Persecution of Old Believers *
When the Russian Orthodox Patriarch introduced sweeping liturgical changes in the seventeenth century, not everyone was happy. A group splintered from the main church, and became known as the Old Believers. The Russian Church, which was closely aligned with the government, would not tolerate the schism, and and an often brutal period of persecution began. This didn't end until 1905, when the Tsar Nicholas II issued an edict of religious tolerance.
* Pogroms in the Russian Empire *
Certain antisemitic tendencies developed in select parts of the Orthodox Church, particularly in the Russian branch. This often resulted in "pogroms," violent attacks against the Jewish population. These attacks were sometimes promoted by misguided clergy, who advocated vengeance against the so-called "Christ-killers." These episodes are referenced in the musical "Fiddler on the Roof," which you may have seen.
Analysis:
It must be remembered that these events happened in the past, and that the Orthodox Church does not advocate these behaviors. The same must be said about the Western Church. The horrors that you mention took place are in the past, and many leaders have apologized for them since.
What it comes down to, ultimately, is that every religion has had dark chapters. Why? Because human beings are involved. Wherever you find human beings, you will find episodes of sin and corruption. There's no escaping it. These sordid histories shouldn't be used as an indictment against any religion in particular, but rather as a commentary on the darker side of human nature.
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