Rome in the end was a decadent, but brutal empire full of slaves. And to a slave christian salvation sounds great.
But before there was a empire with emperors taking up the idea of becoming gods themself, there was a republic. And also after it became an empire, they did not have a institution like the inquisition shaping thought and banning heresy baked into their system.
This is the fundamental difference that I see.
In medieval times being expelled from the church was pretty much a death sentence. In roman and greek times for most of its existence not really.