You are asking about people from two distinct cultures each spanning centuries. Within that enormous period, one would likely to have found a great amount of diversity in belief.

Frankly, I'm not even sure what "modern Christians" believe. Consider the diversity of that international population. What is it, exactly, that "they" believe? The answer is "all sorts of things, with very little agreement." Any effort to typify the beliefs of Greeks, Romans, or Christians, will stumble for want of an accurate generalization.