The story of Paul
In Galatians 1:15-17, Paul gives us his version of his conversion:
“But when it pleased God, who separated me from my mother's womb, and
called me by his grace, To reveal his Son in me, that I might preach
him among the heathen [gentiles]; immediately I conferred not with flesh and
blood: Neither went I up to Jerusalem to them which were apostles
before me; but I went into Arabia, and returned again unto Damascus.”
Writing several decades before Acts of the Apostles was written, he says that God called him, to preach to Gentiles. His itinerary shows that he immediately set out to do just this. In Damascus, the governor of the city sought to arrest Paul, almost certainly for converting Gentiles, as the governor would have had no interest in religious differences amongst the Jews. Paul escaped from the soldiers by being let down in a basket (2 Corinthians 11:33).
In Romans 15:15-16, Paul makes it clear that he sees his own mission as “the minister to the Gentiles” as special:
“Nevertheless, brethren, I have written the more boldly unto you in
some sort, as putting you in mind, because of the grace that is given
to me of God, That I should be the minister of Jesus Christ to the
Gentiles, ministering the gospel of God, that the offering up of the
Gentiles might be acceptable, being sanctified by the Holy Ghost.”
Elsewhere, he describes Peter as the apostle to the Jews, even showing how Peter was uncomfortable being seen eating with Gentiles.
On the other hand Acts chapters 10-11 tell of Peter realising he was called to preach to Jews and Gentiles alike, and how he baptised the centurion Cornelius and many others. Acts 9:20-25 gives a very different reason for Paul being let down in a basket at Damascus. Paul is preaching to Jews, and Jews alone, and it is the Jews who wished to kill Paul:
And straightway he preached Christ in the synagogues, that he is the Son of God. But all that heard him were amazed, and said; Is not this he that destroyed them which called on this name in Jerusalem, and came hither for that intent, that he might bring them bound unto the chief priests? But Saul increased the more in strength, and confounded the Jews which dwelt at Damascus, proving that this is very Christ. And after that many days were fulfilled, the Jews took counsel to kill him: But their laying await was known of Saul. And they watched the gates day and night to kill him. Then the disciples took him by night, and let him down by the wall in a basket.
These discrepancies can perhaps be explained by the author of Acts wishing specifically to give Peter full credit to Peter for initiating the decision to preach to the Gentiles. John Dominic Crossan speaks for the majority of modern New Testament scholars when he says, in The Birth of Christianity, page 21, Acts of the Apostles is theology rather than history.
The Great Commission
Matthew 28:16-20 tells us that the disciples went into Galilee, as instructed by the angel (28:7), where they met Jesus and received the Great Commission. This was the last time Jesus met the disciples, who spread out to preach the gospel:
Then the eleven disciples went away into Galilee, into a mountain
where Jesus had appointed them. And when they saw him, they worshipped
him: but some doubted. And Jesus came and spake unto them, saying, All
power is given unto me in heaven and in earth. Go ye therefore, and
teach all nations, baptizing them in the name of the Father, and of
the Son, and of the Holy Ghost: Teaching them to observe all things
whatsoever I have commanded you: and, lo, I am with you alway, even
unto the end of the world. Amen.
But Luke says that Jesus met the disciples at a meal in Jerusalem on the evening of his resurrection, telling them to remain in Jerusalem, then led them out to the nearby town of Bethany, where he blessed them and wascarried up into heaven (24:49-53):
And, behold, I send the promise of my Father upon you: but tarry ye in
the city of Jerusalem, until ye be endued with power from on high. And
he led them out as far as to Bethany, and he lifted up his hands, and
blessed them. And it came to pass, while he blessed them, he was
parted from them, and carried up into heaven. And they worshipped him,
and returned to Jerusalem with great joy: And were continually in the
temple, praising and blessing God. Amen.
To explain this difference, it is the strong consensus of scholars that the Gospels of Matthew and Luke were substantially based on Mark's Gospel. However, Mark originally ended at verse 16:8, with the young man telling the women that Jesus was risen and they fled in terror, telling no one. The authors of both Matthew and Luke wished to provide their readers with evidence that Jesus had really risen from the dead but, with no guidance from Mark, each had to create his own ending. Matthew's ending includes the Great Commission, but Luke's does not.
It has been proposed that Acts of the Apostles is, in the words of Crossan, theology rather than history, and that Matthew's Great Commission was a literary creation by an anonymous author otherwise dependent on Mark and the hypothetical 'Q' document for everything he knew about the mission of Jesus. To the extent they are inconsistent with the epistles of Paul, they should therefore be considered doubtful.
Paul's own account in his epistles is generally regarded as substantially reliable. He says that God called him to preach to Gentiles, and his epistles describe him as doing this throughout his mission. Whatever the disciples, other than Peter and John, were doing, Paul makes no mention of ever being in contact with them. He mentions other missionaries, such as Apollos, but never any of the disciples except Peter and John, and James the brother of Jesus.