It doesn't pass the laugh test to claim nothing about society, culture, and ethics really changed between the Greco-Roman world and European Christianity. It is factually inaccurate to claim that is was all basically a continuation of the same thing.
On the downside, Christianity did continue a traditional of patriarchy, as did all societies on the planet.
Christianity did condone violence against perceived heritics and rival religions.
Christianit leaders often found themselves in league with perpetuating the power of the aristocracy.
For a 300 year period, some Christian leaders turned a blind eye to African slavery.
You also cannot overlook the long and toxic history of anti-semitism in Christian history.
On the positive side, Christianity did make certain ethical norms a theologically binding expectation: charity, compassion, humility, the golden rule, universal love. Not to say it was always or consistently practiced, but it was considered a formal religious expectation. The pagan religions of Greek and Rome had no system of ethics. They were strictly sacrificial religions intended to curry favor with the gods. To the extent anyone practiced compassion, it was an individual choice, but it was not a cultural or religious expectation.
The cultural values of the Greeks and Romans were personal courage, valor on the battlefield, personal honor, and personal reputation, and might makes right. This is clearly illustrated in the Illiad, the Odyssey, and the Melian debate.
As to slavery, not a single person in the pre-christian Greco-Roman world ever wrote anything against slavery. Nor did anyone even write anything expressing discomfort with slavery.
Christianity was the first intellectual tradition in the west to start to distance itself from slavery. Saint Augustine, while recognizing slavery was a reality in this world, still wrote that slavery was a sin and a result of the corruption of man's soul. That was a pretty radical thing to say for it's day.
Slavery had disappeared in Christian Europe by the early Middle Ages, to be replaced by serfdom. Which was terrible in itself, but serfdom was not as bad as chattal slavery. Your average chattel slave would trade places with an average serf in a nanosecond.
A lot of Christian leaders did look the other way for three centuries in the early modern era, when European mercantilists and capitalists kicked off the Africa slave trade.
And I would count that, anti-semitism, and patriarchy as Christianity's most significant moral failures