The famous story is that Vladimir received missions and then sent envoys to see for himself. The Bulgars offered Islam and were refused because the Rus cannot do without drink; the Jews of Khazaria were asked where their homeland was and answered that God had scattered them; among the Germans the envoys saw no beauty; and in the great church at Constantinople they did not know whether they were in heaven or on earth. It is a good story and it is a story. It was written down a century or so later by a chronicler with a case to make, and it explains a decision that had already been taken on other grounds.
The other grounds are visible enough. Vladimir sent troops to Basil II when the emperor needed them badly, took the emperor sister Anna in marriage, which was an extraordinary concession, and pressed the point by seizing Chersonesus in the Crimea. What came with the church mattered more than what came with the marriage. The liturgy arrived in Slavonic rather than Greek, because the Bulgarian mission had already translated it, so the Rus received a literary language along with a religion and did not have to learn another one to be Christian. The ecclesiastical link to Constantinople held for centuries, and Vladimir is a saint in both the Orthodox and the Catholic calendars, styled Equal to the Apostles.