Matthew quotes Mark’s fictional narrative word for word, but also adds additional material including a fictional nativity story and a post-resurrection appearance. Matthew’s nativity story is based on the nativity story of Moses as found in the first century book Biblical Antiquities.
Matthew disagreed with Mark’s Pauline Christianity in which circumcision and dietary restrictions were optional, so he rewrote Mark’s story for Torah-observant Christians. Matthew sometimes makes the story more ridiculous as when Jesus enters Jerusalem on two donkeys rather than one. He does this to fit the prophecy of Zechariah 9:9, not because he remembers history better than Mark.
Matthew replaces Mark’s literary structure with one of his own, divided into five sections which alternate between narrative and the five Great Discourses. He also uses a chiastic superstructure and his crucifixion narrative is more elegantly chiastic than Mark’s.
Matthew 1:23 says Jesus will be called Immanuel (which means “God is with us”) even though Jesus is never called this. He does this in order to parallel the ending when Jesus says, “I am with you” in Matthew 28:20. Literary structure like this couldn’t have originated orally.
A lot of sections Matthew adds deal with missionary work and how the church operates. These are issues that would have come up after Jesus died and thus wouldn’t have originated with him. Peter is more prominent in Matthew, reflecting the importance of how the church will function.
The Sermon on the Mount relies on the Septuagint Greek version of Deuteronomy and Leviticus, so it doesn’t go back to a Hebrew or Aramaic source. Matthew also redacts other Greek scriptures like “turn the other cheek” taken from Isaiah 50:6-9. The sermon has a literary structure so it didn’t originate in oral tradition, and it deals with issues that would have come up after Jesus died, so it didn’t originate with him. The sermon also assumes the template doesn’t exist, so it had to have been written after the destruction of the temple in 70 AD. It also addresses the rabbinical argument that followed the destruction of the temple.
Matthew parallels Jesus with Moses. The Five Great Discourses parallel the five books of Moses. The Sermon on the Mount emulates Moses delivering the commandments from Mount Sinai. Jesus’s Great Commission echoes Moses’s Great Commission.
In Mark, Jesus wanders in the wilderness for forty days to parallel the Jews wandering for forty years. Matthew also adds Jesus having the same temptations as the Jews to further the parallel. What Matthew adds to Mark isn’t history, just more myth and literary structure. Thus, Matthew doesn’t count as evidence for either historicism or mythicism.
Luke is the first gospel to claim to be history. He adds in historical details and attempts to date some events. He includes a preface explaining why he is writing. His resurrection narrative attempts to answer skeptics of Matthew’s account. However, the fact that no one knew of any of these details before indicates that they’re fiction.
Luke is not doing history, although he pretends to. He doesn’t weigh facts and check them against independent sources, he’s just rewriting Matthew and Mark to suit his own purposes. He never names his sources or tells us why we should trust them.
Luke borrows heavily from Matthew and quotes him verbatim in places, so the Q theory (that Luke and Matthew both used a now lost document called Q) is unnecessary. Luke changes Matthew, such as changing the Sermon on the Mount into the Sermon on the Plain. He changes the nativity narrative, but copies Matthew’s in some ways. He also changes how Judas dies and the genealogy of Jesus.
Luke attempts to harmonize Mark’s gentile Christianity with Matthew’s Torah-observant Christianity.
Luke used Josephus and Homer as a model, as well as expanding upon Mark’s use of Elijah and Elisha from 1 and 2 Kings. For example, the healing of the widow’s son at Nain doesn’t appear in Mark or Matthew. It’s a typical urban legend of the time (a similar tale is told of Asclepiades by Apuleius and other tales referenced by Pliny the Elder.) Luke’s version is basically a rewrite of a tale of Elijah in 1 Kings 17.
Luke also uses other Old Testament sources. John the Baptist’s nativity is based on Samson’s nativity as told in Biblical Antiquities 42. Mary’s song (the Magnificat) in Luke 1:46-55 is based on Hannah’s song in 1 Samuel 2:1-10.
Luke uses a diptych structure which is often interrupted, which suggests someone else made later additions. Like Mark and Matthew, Luke also uses the Romulus resurrection story, but he expands their versions in his Emmaus narrative. Emmaus also parallels the beginning of Luke. They both take place during Passover and involve a trip to Jerusalem. A couple discover that Jesus is missing (Mary and Joseph in the beginning, Cleopas and his companion in Emmaus). They return to Jerusalem and find Jesus after three days. Jesus asks what they are doing, explains scripture to them, and tells them what he did was necessary. Both these stories first appear in Luke.
In the Codex Bezae, this happens not at Emmaus, but at Oulammaous (God’s House), which matches the father’s house in Luke 2:49. Bezae also seems to contain other more original readings such as it taking twenty men to move the stone in front of Jesus’s tomb to match the twenty men Josephus says it takes to open the temple.
The material Luke adds to Mark and Matthew isn’t likely to be more historical. It’s just more fiction. Thus, Luke is no more probable on either historicity or mythicism.