Matthew was a tax collector and is written to the Jews. The skills of a tax collector included remembering details and taking shorthand, so many believe that Matthew's discourses of what Jesus said are close to the actual words of Jesus. In writing to the Jews, Matthew provides many Old Testament prophecies of Jesus.
Mark is the writer of the Gospel as related to Mark by Peter for publication. Mark appears to add a few personal touches, as was usually done, and probably with the permission of Peter. The Gospel of Mark is often taken as a Gospel of servant-hood, laking a genealogy as in Matthew and Luke. My personal preference is that Peter thought like a scientist, making many observations, making conclusions based on those observations, and leaving out parts that were either assumed to have been known or not relevant for what he was trying to say.
Luke was a physician for Paul. Medical practice was not like we know it today. As a physician, one could often not do much to help the patient. What one could do is ask questions, listen, console, and do limited things to help. Such skills made for an excellent historian. Luke appears to have sought out, questioned, and collected stories that he could verify. If a story is in the other Gospels but not Luke, it does not mean they are untrue. It means that Luke either did not know about them or could not personally verify their validity.
John is sometimes considered a mystic. On the other hand, John approaches problems and explains them in what today is considered a top-down backward-chaining approach that is embodied in the computer/information science of today.
