I think it would’ve taken on more eastern philosophies. Christianity didn’t just replace and engulf the pagans but also put the eastern mysticism at bay, probably would’ve included heavy caste systems like India. Would’ve made what we refer to as the reformations much more difficult.

I think Constantine did Christianity a disservice, though. Brought the church into a position that lead to the tyrannical tendencies that lasted centuries on and off. Makes sense as to why he did, institutionalized religion was just how things were back then and many of the intellectuals were converting. Thankfully Christianity in large brought us out of that.

He wouldn't have moved the seat of the Empire to Turkey. Most likely Constantinople wouldn't exist. The shift to Christianity would have happened differently.

Culturally there would never have been any of the classical movements of art and music. There would be no Mozart, Beethoven...etc. There would have been no Leonardo DeVinci, and no Michaleangelo.
There would only have been a continuation of serfdom and slavery. There would never have been a "Court of The Star Chamber" and therefore no Magna Carta and no United States Constitution. Technological development of astronomy, physics, chemistry and medicine likely would not have taken place.

What if we still lived under a Roman culture without Christianity? Slavery would still be a prominent practice, women would not directly participate in elections, I'd imagine a racially segregated caste system would be in place, government would not recognize individual freedoms, and scientific rationalization would be severely constrained to superstition.

Why do I think this? Because this is how the rest of the world behaves outside of the influence of Christendom.