Passover and the Passion
The Synoptics set the Last Supper on Passover night; John places the crucifixion on the day of preparation, when the Passover lambs were slaughtered (John 19:14, 19:31).
John 19:14-16
14Now it was the Preparation Day of the Passover, at about the sixth hour. He said to the Jews, “Behold, your King!”
15They cried out, “Away with him! Away with him! Crucify him!” Pilate said to them, “Shall I crucify your King?” The chief priests answered, “We have no king but Caesar!”
16So then he delivered him to them to be crucified. So they took Jesus and led him away.
Mark 14:12-16
12On the first day of unleavened bread, when they sacrificed the Passover, his disciples asked him, “Where do you want us to go and prepare that you may eat the Passover?”
13He sent two of his disciples, and said to them, “Go into the city, and there you will meet a man carrying a pitcher of water. Follow him,
14and wherever he enters in, tell the master of the house, ‘The Teacher says, “Where is the guest room, where I may eat the Passover with my disciples?” ’
15He will himself show you a large upper room furnished and ready. Get ready for us there.”
16His disciples went out, and came into the city, and found things as he had said to them, and they prepared the Passover.
What each tradition says
Rabbinic / Midrashic
According to the Jewish Encyclopedia, John’s Gospel, whose author seems to have had access to trustworthy traditions about the last days, presents the priests hurrying the trial to avoid acting on the festival, which according to this began Friday evening. The source adds that this view may reflect a desire to make Jesus’ death symbolize the paschal lamb sacrifice.
Joseph Jacobs, Kaufmann Kohler, Richard Gottheil, Samuel Krauss, The Jewish Encyclopedia (Funk & Wagnalls, 1901-1906), s.v. 'Jesus of Nazareth' — section 'The Last Supper'
Patristic
Chrysostom asks what "That they might eat the Passover" means, since Christ had done this on the first day of unleavened bread. He says either the whole feast is called "the Passover," or they were then keeping Passover, while Christ delivered it to His followers one day sooner.
John Chrysostom (c. 349-407), Homilies on the Gospel of St. John, in NPNF ser. 1, vol. 14 (ed. Philip Schaff; T&T Clark, Edinburgh, 1889) — Homily LXXXIII, section 3 (on John 18:28, 'that they might eat the Passover')
Catholic
Aquinas holds that John's phrase "Before the festival day of the Pasch" refers to the fourteenth day of the moon, which then fell on Thursday. The fifteenth day was the Jews' most solemn Pasch, so what John calls before the festival, Matthew calls the first day of unleavened bread, since the Jewish solemnity began the preceding evening.
Thomas Aquinas (1225-1274); trans. Fathers of the English Dominican Province (1920), Summa Theologiae, Second and Revised Edition (New Advent) — III, q.46, a.9 ('Whether Christ suffered at a suitable time'), reply to objection 1
Orthodox
John of Damascus speaks of the upper chamber of holy and illustrious Sion. There, after He had eaten the ancient Passover with His disciples, He fulfilled the ancient covenant.
John of Damascus (c. 675-c. 749), An Exact Exposition of the Orthodox Faith, in NPNF ser. 2, vol. 9 (trans. S. D. F. Salmond; T&T Clark, Edinburgh, 1898) — Book IV, ch. 13 (Concerning the holy and immaculate Mysteries of the Lord)
Reformed / Protestant
Calvin has no doubt that Christ observed the day appointed by the Law, and that the Jews followed a custom long in use. He notes Christ was put to death the day before the Sabbath, and that it was universally admitted that by ancient custom, when the passover fell on Friday, it was delayed till the following day.
John Calvin (1509-1564), Commentary on a Harmony of the Evangelists, Matthew, Mark, and Luke, vol. 3 (trans. William Pringle; Calvin Translation Society) — On Matthew 26:17-19, in the section covering Matthew 26:14-20; Mark 14:10-17; Luke 22:3-14
Evangelical
Albert Barnes notes that the Pharisees used various methods to determine when the month began, including witnesses and astronomical calculations. From this, a difference arose about the time of Passover, and Jesus kept it one day sooner than most of the people.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on Matthew 26:18 (the parallel to Mark 14:12-16)