Why wasn't the Eastern Orthodox church ever as violent and murderous as the Western C

Was there something in their theology that made them better?

They were..but had a better press agent!

who says they were not?

The theology is basically the same.

It was the politics of the Rome: the Popes envisioned themselves as emperors over emperors, they dictated Western European policies.

Eastern Orthodox Patriarchs were always the leaders of the Church only in their countries. They could influence internal policy, but only the monarchs could be the decision makers.

Another factor.
Historically, the Eastern European people are more tolerant to other cultures because they've had less competition over the "living space": they always had plenty of land and water resources.

Yes, the Eastern Orthodox church has not deviated from the teachings of Christ and the holy Canons and Traditions unlike the secular Roman Catholics.

You really should not ask a loaded question that makes the highly disputed presupposition "as violent and murderous as the Western Catholic one."

This loaded question is a logical fallacy, like the old unjust leading question, "Have you stopped beating your wife?"

This type of fallacy is called Plurium Interrogationum, which in Latin means "many questions" and is a question with a false, disputed, or question-begging presupposition.

For more information on loaded questions, see: http://www.fallacyfiles.org/loadques.html

With love in Christ.