Christianity offers a personal relationship with a God that cares about you personally. In Paganism the gods don’t really care about you but can sometimes be bribed to help you out.
The Christian God is love, kindness, and mercy. He rewards the good, punishes the evil. In Paganism the gods are fickle, uncaring, and generally act like ordinary humans with super powers.
Christianity is accessible. People are encouraged to participate and form networks of believers who help each other out both materially and spiritually. Paganism offers nothing of the sort.
Christianity has a set of concrete beliefs that can easily be explained. Paganism has no real beliefs other than pleasing the Gods via prayer and sacrifice.
Christianity has a very well organized network of priests, deacons, elders, bishops, and so on. The write to each other, help each other out, and are part of one faith. Pagan priests are civil servants who do nothing but hang around the temple and participate in festivals. There is no network of religion and no one person you can point to as being in charge, even resonates.
Christianity encourages love, kindness, mercy, and so on. This results in tangible benefits for those in need, which is doubly important when there is no social safety net. Paganism sees mercy as weakness and a live for one’s enemies as foolish.
Christianity is very visible. Ancient authors comment that while Christians are in the plague-ridden slums taking care of the sick, dying, and dead, the Pagan priests are nowhere to be found and there are no organized networks of Pagan charities.
Christians are willing to undergo a great number of privations and hardships such as torture and execution in the arena rather than abandon their faith. This is a visible sign of the strength of the faith that in a world where there are nearly infinite gods to choose from, Christians have just the one and no amount of torture can dissuade them.
The role of women is much expanded in Christianity than in Paganism or Judaism. While good Roman women are meant to be cloistered at home and have very few freedom and opportunities, early Christianity offered women a role which would have been unthinkable to Pagans and Jews.
Christianity was a religion which was disproportionately popular amongst the elite. Typical conversion patterns are a female aristocrat converting to Christianity, then a few members of her household, and then her husband and male relatives. When you see a bunch of powerful people all doing the same thing, not only does it seem like a good idea but it can actually lead to better prospects and opportunities.