"The promise of an easy life" was not a reason that people moved west in the late 1800s, since in fact many people knew that this new life would be quite dangerous and difficult.
The rise of christianity in the Roman Empire was different to that of medieval Europe.
In the Roman Empire, christians were persecuted at the beginning and very slowly increased the amount of people who believed in their god. However, as time passed, more and more people identified themselves as belonging to the christian religion.
In medieval Europe on the other hand, christianity became popular much faster, as there was not that much opposition, compared to the times of Roman empire.