In the Matthew passage, Peter and Andrew are together fishing. In the John passage, Andrew was with John the Baptist and Peter was else where?
I don't see an inherent conflict between these passages. Specifically, the John passage describes how both Andrew and Simon initially met Jesus; the Matthew passage describes how He called them as disciples. Matthew never claims that the event by the seashore was Jesus' first encounter with the brothers.
Edit: In the account of John, Peter meets Jesus just after Jesus had been baptized, been tempted in the wilderness, and came back (John 1:32-34). Peter's calling is in all of the gospels. In Luke, Jesus was tempted in chapter 4. Afterward, in chapter 5 (coinciding with the chronology in John 1), he calls Peter as a disciple (his calling is paralleled in Matt 4 and Mark 1). In Luke 4:38-39, just before Peter and Andrew were called, Jesus went from the synagogue to the house of - wait for it - Simon! He went to heal His mother in law! This is before Jesus called him as a disciple. Also, in 5:3, he first refers to Peter simply by the name of Simon, just like in 4:38, so we can safely assume it is the same Simon whose house He had visited (otherwise Luke should have/would have given him a distinction, like Simon the fisher, in order to clarify it wasn't the Simon discussed only about ten verses ago in chapter 4, right?) Jesus called him after healing his mother in law! Of course He could have met Him as discussed in John 1 with his actual calling taking place soon after! Does anybody see a flaw or hole in this line of logic?