I thought Judaism isn't too fond on actively seeking converts? I could be 100% wrong here though, but I thought that was one of the main differences between Christianity and Judaism at least in the beginning.
Again, I might have no idea what I'm talking about...
Yeah didn't think that Judaism took on too many converts.
Though that might explain how there were so many Jews in the Roman empire
Actualy, the Judaism's reluctance to take on converts was a product of the Christianization of the Empire.
After Constantine's conversion, and then Theodosius reign it became increasingly hard for Judaism to accept converts.
For example, it became illegal for a Jewish man to own a Christian slave. It also then became illegal for a Jewish man to circumcise his slaves. This of course was of immense importance to the Jewish people since the Covenant demands that ALL male members of a Jewish man's household must be circumcised.
Active discrimination (not progrom levels) came just a little later. One of the reasons for this is that Judaism and Christianity in the first centuries CE were not clear cut.
Many people existed in a middle area. People would practice Jewish customs but believe in Jesus Christ. Christians would go to Jewish synagogues etc etc. Thus, BOTH sides of the divide sought to define themselves. Christian authorities sought to actively seperate the two populations and define itself beyond its Jewish roots. Judaism, once the Rabbis took a firm hand on the religion, emphasized itself as an ethnic religion rather than a prosletizing one and settled in for the long haul. This trend in Judaism was only further emphasized once the Muslims overan the Eastern Roman Empire and the Sassanids.
Christian conversion practices, not surprisingly, took alot from Jewish ones. They both appealled to powerful women (often widows) and through them their households and their lines of patronage.
Christianity just took what Judaism did and did it better by appealing to men more effectively as well. One of the things the Romans found distastefull about Judaism was circumcision. They viewed it as the equivalent of being castrated at times. Christianity's ditching of Jewish religious law helped them appeal to the general masses, though again, it should be pointed out that many Christian converts did enter that grey area between Christianity and Judaism.
EDIT: One thing to note, if any sufficiently monotheistic religion takes firm hold of the Empire, competing faiths will be discrimated against. For any sufficiently prosletyzing religion, competition will not be tolerated. The surviving ones will often redefine themselves along more exclusivistic grounds. For examples, see Judaism under Christianity, Zoroastrianism under Islam, and even certain Christian sects in very not Christian environs such as India (Take Floccuencio for example: I believe he is from a Syriac Christian familly in Kerala. From what I understand, they are sort of an ethnic group as much as a religious one).
Ergo, if a different religion other than Christianity takes the helm (such as Manicheanism or Isus), depending on the POD you would probably see Christianity take a similar path to Judaism. You might not even see either really survive seperately, but instead merge into a middle area... like Messianic Jews (this is to point out that modern Rabbinical Judaism was not set in stone during the early centuries CE)