Judaism is not a proselyting religion, so it limits its own spread. Either you are born a child of Abraham or you are not. Historically, Judaism has always remained relatively small. Although people could convert, they were never actively sought, and proselytes were never considered quite as good as the real thing. Christianity, on the other hand, was opened up to gentiles and actively sought converts. The apostles, the seven deacons, and the seventy were all active missionary groups that preached that Jesus was the Messiah. As you probably know, belief in a Messiah was already an idea spread amongst the Jews, so preaching that he would deliver from sin instead of Roman oppression wasn't too big a transition among Jewish crowds. Also, there was much appeal among the poor, as Christianity taught that all were alike before God, that he that abaseth himself shall be exalted, that Jesus himself reached out to the outcasts, etc. It was tolerated among the Roman Empire until Rome burned under Nero and he needed someone to blame it on. Christians were severely persecuted and often executed, but still the message found appeal. Once Constantine became Emperor and converted to Christianity, he made it the state religion and suddenly elevated this downtrodden religion to an exalted status. Christianity, by virtue of being essentially one and the same as the most powerful Empire Europe had ever seen, then spread even more rapidly and had political and military power to back it up. It was guaranteed success.

And there's also the fact that I, a believing Christian, think God had a hand in preserving it all.

That's all off the top of my head. Hope it helps.