GraceSeeker, I understand that you must have voted for option #3 "Peter and the other disciples". Would you mind commenting on my post on page one concerning Paul and Galatians? In this letter I see a rift between Paul and the disciples of Jesus (as) over circumcision and following the Judaic Law. The "Gospel" preached by Peter to the Jews, though perhaps similar, was obviously not identical to the "Gospel" preached by Paul to the Gentiles. Which "version" of Christianity won-the-day such that we have it today.
I think the answer to your final question, which "verision" won the day, is clearly spelled out in Acts 15:
1Some men came down from Judea to Antioch and were teaching the brothers: "Unless you are circumcised, according to the custom taught by Moses, you cannot be saved." 2This brought Paul and Barnabas into sharp dispute and debate with them.
This seems to be the same conflict that Paul references in Galatians 2. Now, Luke's accounting of the way that conflict was handled and Paul's vary -- I suspect some bombacity on Paul's part in the telling, he just often strikes me that way, especially when it comes to things that touch upon him personally. Luke on the other hand comes across as the more disinterested reporter of events. But, I also don't think that Luke was actually present, so it may be the Luke is telling a sanitized verision of the conversations that he terms were a "sharp dispute". I suspect the actual historical events lay someplace between.
But as for what became the acceptable standard for the church, that is provided by James in Luke's telling of it:
Acts 15
19"It is my judgment, therefore, that we should not make it difficult for the Gentiles who are turning to God. 20Instead we should write to them, telling them to abstain from food polluted by idols, from sexual immorality, from the meat of strangled animals and from blood. 21For Moses has been preached in every city from the earliest times and is read in the synagogues on every Sabbath."
22Then the apostles and elders, with the whole church, decided to choose some of their own men and send them to Antioch with Paul and Barnabas. They chose Judas (called Barsabbas) and Silas, two men who were leaders among the brothers. 23With them they sent the following letter: The apostles and elders, your brothers, To the Gentile believers in Antioch, Syria and Cilicia: Greetings. 24We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said. 25So we all agreed to choose some men and send them to you with our dear friends Barnabas and Paul— 26men who have risked their lives for the name of our Lord Jesus Christ. 27Therefore we are sending Judas and Silas to confirm by word of mouth what we are writing. 28It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: 29You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things. Farewell.
In other words, there is no requirement for Greeks to become Jews in order to be part of the Church. You might think that this is Paul winning the argument. It certainly is the position he was championing. But it is important to note the Acts 10 & 11 shows that it was already the position of Peter. I can even see this in Paul's reference to Peter as a hypocrite in the passage you cite. Paul calls Peter a hypocrite becaue Peter "used to eat with the Gentiles", and then drew back from that practice when these Judaizers arrived. So, I am suggesting the Paul's position that does win the day is nothing new with Paul. It already existed with Peter and Peter had introduce this to the practice of the church before Paul did. However, there were still those that challenged the idea, and apparently embarrassed Peter into behaving like a hypocrite. And in that situation, Paul was more willing to stand up for the gospel than Peter was, but it was not Paul's invention, rather it was one that he and Peter shared, and Paul was less willing to back down.
Given that difference between them, it makes sense that Paul would be the one to take the Gospel to the Gentiles while Peter would take it to the Jews.
However, note what happens when Paul begins his next missionary journey to the Gentiles. On the heals of the Council in Jerusalem and some time back in Antioch, where the problem arose, Paul sets out to return to the Greek communities he previously visited. Only this time Timothy joins him:
Acts 16
2The brothers at Lystra and Iconium spoke well of him [Timothy]. 3Paul wanted to take him along on the journey, so he circumcised him because of the Jews who lived in that area, for they all knew that his father was a Greek.
So, here we have Paul being the one who capitulates.
What this all says to me is that there was a lot more give and take in the early church than we project on it today. They didn't have a clearly defined road map of where they were going. They just sort of found there way. Different people provided different types of leadership in different situations. Paul clearly was among the valued leaders and has had a long-lasting influence. But it wasn't just Paul. It was many others, and those others were nearly all on the scene before him. It was as he described himself, one "untimely born" (1 Corinthians 15:8, NASB) or "one born out of due time" (KJV), "born at the wrong time" (CEV).
But as to what the message was, Paul preached what he termed the "gospel", it was not a record of Jesus' teachings, it was rather the story of Jesus' act of bringing salvation to lost people:
1 Corinthians 15
1Now, brothers, I want to remind you of the gospel I preached to you, which you received and on which you have taken your stand. 2By this gospel you are saved, if you hold firmly to the word I preached to you. Otherwise, you have believed in vain.
3For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, 4that he was buried, that he was raised on the third day according to the Scriptures, 5and that he appeared to Peter, and then to the Twelve. 6After that, he appeared to more than five hundred of the brothers at the same time, most of whom are still living, though some have fallen asleep. 7Then he appeared to James, then to all the apostles, 8and last of all he appeared to me also, as to one abnormally born.
9For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God. 10But by the grace of God I am what I am, and his grace to me was not without effect. No, I worked harder than all of them—yet not I, but the grace of God that was with me. 11Whether, then, it was I or they, this is what we preach, and this is what you believed.
That last line is worth repeating--"Whether, then, it was I or they, this is what we preach, and this is what you believed." The accounting from Acts shows that Paul is on the same page with all the other disciples, and here Paul's own telling of the Gospel does the same as well.
There was indeed a "rift" as you put it, but I don't think that it was worked out by one "version" winning the day over another. Rather, the church worked under the guidance of the Spirit to see what it was that God was doing, from Peter's interaction with Cornelius, to the response to Paul's preaching to Gentiles, and then affirmed what was already the practice of both, that Gentiles did not need to become Jews to find salvation. It was those who sought to make Jews of everyone that were told they did not represent the views of the apostles, and neither Peter nor Paul were in that group that opposed the teaching of the apostles on this matter.