Constantine changed the Church's circumstances a great deal. The settlement of 313 gave Christians and everyone else freedom of worship, he enriched and adorned churches, and he took part in a council of bishops, where, according to the Catholic Encyclopedia, his presence was meant to show his interest rather than to decide the outcome. He was baptized only at the end of his life, in 337. Historians, and Orthodox and Protestant Christians, weigh the early evidence differently from Catholics, especially on how the authority of the bishop of Rome was exercised in the first centuries; the texts above show that a Church with bishops, a Eucharist understood as Christ's flesh and the name "Catholic" existed long before any emperor was Christian.
Rome shows both halves of the story. What Constantine did do is still standing: Benedict XVI recalled that he gave Pope Miltiades the old property of the Laterani family and built there the basilica, the baptistery and the residence of the Bishop of Rome. That basilica, St. John Lateran, was dedicated by Pope Sylvester I on November 9, 324 and remains the cathedral of Rome. He also built the first St. Peter's over the grave already venerated as the Apostle's. What is older than Constantine is there too: the Christian catacombs along the roads out of the city, and the cemetery beneath St. Peter's.