While the Christian states were discriminatory toward non-Christian religions, they were not generally engaged in genocidal mania toward groups. With the modern totalitarian regimes, such as the Nazis, they could not tolerate a group, even if it was made to be severely disadvantaged; they simply said, "Kill all of them." If the Christian Emperors had wanted to kill all the Jews in the Byzantine Empire, especially before the conversion of the Khazar Empire to Judaism, they could have easily done so. Perhaps not on an industrial scale, but, it could have been done, since everyone knew where the large Jewish populations where (Thessalonika, etc). However, they choose not to do that, but, instead, to generally follow the advice of St. Augustine and others, and place the Jews as a religious group (though not as an ethnic group, since conversion lifted the situation) under legal disabilities. For example:http://en.wikipedia.org/wiki/Jews_in_the_Byzantine_Empire
It wasn't complete freedom of religion, and they were subject to state discrimination, and periodic persecutions, but, it certainly wasn't the Holocaust, nor was it even comparable to the blood letting under the Diocletian period, especially the horrific time in Palestine (see Eusebius of Caesaria).
Also, Paganism was a dying force, and it could not theological compete with Christianity; you only find the more sophisticated non-Christian 'pagan' Neo-platonists, surviving. Many of them left to the Persian Empire after Justinian closed down the Academy, but, they found themselves in a far worse situation there, and were allowed back into the Empire.
I think we should not compare the state enforced disabilities and discriminations, and occasional persecutions found, in, let's say the Eastern Empire, to that which the Nazis did. For one, they were not as violent. Two, their aims were completely different. Three, the Nazis didn't care if you were a Jew who had become a Christian, it was a 'racial' question to them. Fourth, the Nazis plan was to kill every last one of their enemies (Jews, Gypsies, Serbs, kill and partially enslave the Slavs), the Empire idea was to just hem the non-Christian groups in, in order to maintain the concept of what would later be called, "Cuius regio, eius religio".
But, again, it wasn't right, but, then again, it was no where the intention of what the Nazis did, or what the Communists did in Russia.
I'm sure there are other cases of less or greater degrees of this.