I think that the main feature of the Catholic Church that excites the intellect of many is its mysticism--the Catholic Church, as far as I know, is the only Christian Church that believes in the
transubstantiation--that part of the Mass where the Eucharistic wafer and the wine
become the body and blood of Christ--it is not merely a symbolic re-enactment--it is a sacrament--only baptized Catholics who have received the sacrament of Holy Communion (now called Eucharist) are permitted to receive communion in a Catholic Church.
Plus we have a lot of great art including beautiful churches all over the world. Also St. Thomas More, Aquinas, Pascal, de Chardin, and other great theologians.
the Catholic Church, as far as I know, is the only Christian Church that believes in the transubstantiation"""
Eastern Orthodox believe in something akin to transubstantiation. Many Anglicans do as well.