Prolegomena
The Transfiguration of Christ, in the New Testament, is an event traditionally understood as the revelation of the glory of Jesus Christ as the Son of God. Described in Matthew 17, Mark 9, and Luke 9, it occurs when Jesus takes his disciples Peter, James, and John to a "high mountain" (traditionally, Mount Tabor): "And he was transfigured before them, and his face shone like the sun, and his garments became white as light" (Matthew 17:2). At the same time, the prophets Moses and Elijah appeared next to Christ and were visible to the disciples and a "voice from the cloud" said: "This is my beloved Son, with whom I am well pleased; listen to him" (Matthew 17:5).
The Transfiguration In the New Testament
The Transfiguration of our Lord on a "high mountain apart," is described by each of the three evangelists (Matt. 17:1-8; Mark 9:2-8; Luke 9:28-36), and none of them mention the name of this mountain. The fullest account is given by Luke, who, no doubt, was informed by Peter, who was present on the occasion. What these evangelists record was an absolute historical reality, and not a mere vision. The concurrence between them in all the circumstances of the incident is exact. John seems to allude to it also (John 1:14). Forty years or so after the event Peter distinctly makes mention of it (2 Pet. 1:16-18). In describing the sanctification of believers, Paul also seems to allude to this majestic and glorious appearance of our Lord on the "holy mount" (Rom. 12:2; 2 Cor. 3:18). The place of the transfiguration is supposed by most scholars today to be Mount Hermon, and not Mount Tabor, as is commonly supposed.
The Case Against Mount Tabor As the Sight of Christ's Transfiguration
Henry Alford (1808) first cast doubt on Tabor in modern times due to the possible continuing Roman utilization of a fortress which Antiochus the Great built on Tabor in 219 BC, and which Josephus records was in use by the Romans in the Jewish War. Others have countered that even if Tabor was fortified by Antiochus this does not rule out a transfiguration at the summit.
John Lightfoot rejects Tabor as too far, but rather "some mountain near Caesarea-Philippi". The usual candidate in this case is Mount Panium, Paneas, or Banias, a small hill situated at the source of the Jordan, near the foot of which, Caesarea Philippi was built.
R. T. France (1987) notes that Mount Hermon is closest to Caesarea Philippi, mentioned in the previous chapter of Matthew. Likewise Meyboom (1861) identified "Djebel-Ejeik," but this may be a confusion with Jabal el Sheikh, the Arabic name for Mount Hermon.
Edward Greswell (1834) raised the possibility of either Tabor or Mount Nebo where Moses viewed the promised land. H. A. Whittaker (1987) proposes that it was Nebo primarily on the basis of the Moses precedent and a parallelism in Jesus' words on descent from the mountain of transfiguration; "You will say to this mountain (i.e. of transfiguration), ‘Move from here to there,’ (i.e. the promised land) and it will move, and nothing will be impossible for you."
In summary:
1. The Gospels record that Jesus was in the vicinity of Caesarea Philippi before the Transfiguration (Matt 16:13). Nothing suggests that he traveled southward to Mount Tabor.
2. The event was intentionally private, and a setting on Mount Hermon or even in the mountains of Upper Galilee would be more suitable than a location on Mount Tabor. The international highway traveling through the Jezreel Valley passed next to the Mount Tabor and would have made privacy unlikely.
3. A military fort on the summit of Mount Tabor during Hasmonean and Roman times was probably in use during Jesus’ ministry and would have precluded the site as a get-away for Jesus.
The Case For Mount Tabor As the Sight of Christ's Transfiguration
Already in Apostolic times the mount of the Transfiguration had become the "holy mount" (2 Peter 1:18). It seems to have been known by the faithful of the country, and tradition identified it with Mount Tabor. Origen said (A.D. 231-54): "Tabor is the mountain of Galilee on which Christ was transfigured" (Comm. in Ps. lxxxviii, 13). In the next century St. Cyril of Jerusalem (Catech., II, 16) and St. Jerome (Ep. xlvi, ad Marcel.; Ep. viii, ad Paulin.; Ep. cviii, ad Eust.) likewise declare it categorically. Later St. Proculus, Patriarch of Constantinople (d. 447; Orat. viii, in Transfig.), Agathangelus (Hist. of Armenia, II, xvii), and Arnobius the Younger (d. 460; Comm. in Ps. lxxxviii, 13) say the same thing. The testimonies increase from century to century without a single dissentient note, and in 553 the Fifth Council of Constantinople erected a see at Mount Tabor (Antiochian Patriarchate). By 570, three Byzantine churches are recorded as standing on Mt. Tabor, or perhaps one large church with chapels dedicated to Christ, Moses and Elijah.
Some modern writers claim that the Transfiguration could not have taken place on Mount Tabor, which, according to Josephus, was then surmounted by a city. This is incorrect; the Jewish historian speaks neither of a city nor a village; he simply fortified, as he repeats three times, "the mount called Itabyrion" ("Bell. Jud.", II, xx, 6; IV, i, 8; Vita, 37). The town of Atabyrion of Polybius, the Tabor or Celeseth Tabor, the "flank of Tabor" of the Bible, is situated at the foot of Mount Tabor. In any case the presence of houses on a wooded height would not have made it impossible to find a place apart.
It is again objected that Our Lord was transfigured on Mount Hermon, since He was at that time in its vicinity. But the Synoptics are all explicit concerning the lapse of time, six days, or about eight days including those of departure and arrival, between the discourse in Cæsarea and the Transfiguration, which would infer a somewhat lengthy journey. Moreover the summits of Hermon are covered with snow as late as June, and even the lesser peaks of 4000 or 5000 feet are likewise snow-covered in February and March, the period of the Transfiguration. Finally, the ancients judged the height of mountains by their appearance, and Tabor especially was considered a "high mountain", if not by David and Jeremiah, at least by Origen and St. Jerome and the pilgrims who made the ascent (500m above the Jezreel Valley).
Supernatural Confirmation In Favor of Mount Tabor
More can be read on this, with the appropriate links to various articles, at the post titled: The Miraculous Holy Cloud of Mount Tabor.