There are dozens of reasons it is important to know the difference of Peter and Paul’s ministries. It is the difference between Catholicism (built on Peter) and Protestantism (built on Paul – as Martin Luther discovered “Justification by Faith alone” by reading the first epistle of Paul in the Bible, the book of Romans).
Acts 13:24 John “Preached baptism” but in I Corinthians 1:17,18 Paul “Preached the Cross.” Before Paul, no one preached the “Good News” of the Cross. In Matthew 16:21,22; Luke 18:31-34 it is clear that the Apostles, during the life and ministry of Jesus Christ on earth, did not even know that he was going to die. Yet in Matthew 10:5-10 they were sent out to preach. They surely did not preach “the Blood,” “the Cross”!
Well, before I keep going, just a couple more thoughts. The differences between Peter and Paul, the Gospel of the Kingdom and the Gospel of the Grace of God, and the failure of the average Bible student to recognize the differences is the reason why there are so many churches and denominations. They all start the Church – the Body of Christ at the day of Pentecost but none actually practices “having all things in common.” They pick and chose which part of Pentecost they want to follow. They should pick none and follow Paul. Also, not only is the gospel clarified by keeping Israel’s program separate from the Body of Christ, but as well by knowing what God is actually doing and accomplishing today will clarify what God’s will and ministry is for us. If we preach the wrong gospel, or practice the wrong will of God we will not be approved and will be ashamed someday at the judgment seat of Christ – see II Timothy 2:15 and I Corinthians 3:10-12.