One thing that I'm pretty sure of is that European or "Western" culture as we know it is not going to exist. Depending on what you think of Euro-western culture, that could either be a bad thing or a good thing.
Ultimately, that will depend on what replaces it, I guess.
Though Christians were certainly as capable of cruelty as any other group, I think that it may be considered significant that certain versions of Christianity was, as far as I know, the only religious movements in history to unequivocally comdemn slavery as evil.
It was the Cynic school that taught that *all* power relationships among humans were to be rejected (the Cynics did not deal in terms of 'evil', but I'd say that is fairly clear). And Caius wrote (with that very familiar mixture of disquiet and regret common to the profiteers of injustice, one imagines) that slavery was 'an institution of the law of nations contrary to natural law'. The Stoics believed that a slave was as human and as deserving of human consideration as his master, but though they considered manumission a virtuous act, they did not advocate the abolition of the system (which really puts them closest to mainstream Christianity at the time). The one thing in the Christian social ethic of Antiquity that is radically new is the concept of charity for heavenly reward.
There is a school of thought which argues that the modern western conception of each individual human having great worth apart from whatever group this person is born into derives ultimately from the Christian view of each individual human soul having great worth apart from visible, worldly considerations. If this is true (which is of course debatable), at least one interpretation of the Christian world view may have been a vital component in the idea both individual rights and universal human rights.
Any serious student of Antiquity will be able to trace the development of most aspects of Christian ethics from the culture that this faith took root in. Thus the real question will have to be what effect the absence of Christianity will have on the cultural makeup of Europe. If the Ancient world develops any kind of cultural continuity, we may well see a somewhat similar system emerge. If not, we're probably a-Viking till the Chinese come.