What did early Christianity have in common with the mystery cults? Did it differ from them or not?

Answer 1

It differed in that it had Judaic roots rather than Graeco-Roman roots, and in that it did not have so many initiatory secrets (although the Lord's Supper could be considered a ritual initiation).

(Personally, I think Paul's contributions to early Christianity were substantially derived from Greek mystery religions, but that's just me. Other scholars may differ.)

It was the same in that it offered community (fictive kinship), the opportunity for religious ecstasy, and a free lunch.