We have seen how, after Nicea, Christianity became the official religion of the Roman Empire. But what about the Jews?
In 70 AD, after a bitter rebellion, the Romans destroyed the Temple in Jerusalem. The rebellion lasted from 66 AD to 73 AD. According to both Tacitus and Josephus 1.1 million Jews died and 97,000 were sold into slavery. (Personally, I think this figure is over-stated and that Tacitus accepted Josephus as his source. But regardless of the exact numbers, there was a tremendous loss of life.) It was a devastating blow to the Jews in the Holy Land.
In 132 AD, Bar Kochba led a second unsuccessful rebellion against the Romans, that ended with the mass suicide at Masada. Bar Kochba and his followers killed themselves rather than face crucification at the hands of the legions. Thousands of Jews, perhaps over a half million, were killed and thousands more taken as slaves. "So glutted was the slave market that a Jew was sold for less than a horse."
The devastation following these revolts effectively ended Israel as a nation for almost 2000 years.
Jews were dispersed throughout the Roman Empire, the second Diaspora. Jewish communities formed in many cities, the largest in Rome itself. Under Rome are Jewish catacombs, similar to the Christian catacombs. There were Jewish communities in Syria, particularly in Antioch, in Turkey, in Asia Minor, and throughout the Italian peninsula. Jews spread into Gaul (France) and Spain.
These Jewish communities were largely separate from the Gentile communities in which they existed. In Ostia, for example, a recent archaeological discovery shows how the Jews lived. Near the harbor is a small building, a synagogue or meeting place, from the Greek word meaning "to bring together." It had an assembly hall (presumably used for prayer,) a kitchen and a dining room. The Jews stayed separate in order to maintain their identity and way of life. Converting non-Jews was never a goal of Judaism.
Anti-Semitism also enforced Jewish separatism. The Emperor Constantine refers to Jews as "impure beings" who are members of an "unclean and pernicious sect". He limits Jewish rights, forbids Jewish religious worship. Conversion to Judaism is made illegal. See http://en.wikipedia.org/wiki/History_of_anti-Semitism#201_to_500
When the council of Nicea changed the date of Easter, they not only wanted to appeal to the pagan sun-worshipers, they also wanted to separate Christianity from its Jewish roots. "We desire, dearest brethren, to separate ourselves from the detestable company of the Jews... How, then, could we follow these Jews, who are almost certainly blinded."
In 363, the Emperor Julian allows Jews to return to "holy Jerusalem which you have for many years longed to see rebuilt". But in 399, Flavius Augustus Honorus confiscates the gold and silver that had been collected in synagogues for the purpose of rebuilding the city. In 415, Jews are accused of conducting ritual murders during Purim (the holiday that celebrates the salvation of the Jews in Babylon by Esther, who would become queen) and synagogues are burnt in Antioch and Magona. The Bishop of Alexandria, who would be canonized as St. Cyril, forces his way into a synagogue, expels the Jews of that city and gives their property to the mob. In 418, the first forced conversions of Jews are recorded by the Bishop of Minorca.
And so it goes. See http://en.wikipedia.org/wiki/History_of_anti-Semitism#201_to_500 for details. Judaism was never going to offer competition to Christianity. The Jews, when left to their own devices, lived in separate communities and did not attempt to convert Christians or pagans. (There are some exceptions, of course, but my point is that Judaism was not a challenge to Christianity for the hearts and minds.) But you will find, in the history of the first centuries of the Christian church, act upon act of violent anti-Semitism conducted not by Christians acting outside the church, but by high-ranking officials of the Church itself.