What is the doctrinal significance of repetition between the Gospels? The four Gospels each cover roughly the same events, but the details differ, as illustrated here.

Leaving aside the difference in similarity between the Synoptic Gospels and John, is there significance to which events are described multiple times?  Are multiply-described events more important in some way, or are they areas where multiple tellings are more important to understand the relevant doctrine?
Deuteronomy 19:15(NIV)


  One witness is not enough to convict anyone accused of any crime or
  offense they may have committed. A matter must be established by the
  testimony of two or three witnesses.


The above verse is a biblical basis to understand a reason for the different gospels. Also the three first gospels were written with different audience in mind:

Matthew wrote with Jews in mind, in Hebraic with Eusebius, Origen and scholar Jerome to testify this.

Mark wrote with non-Jews in mind. For example Latin terms are used, contains explanations that would not have been necessary for Jewish readers and also explain Semitic terms.

Luke wrote it for Theophilus (Luke 1:1-3)

John provide more information for events that the other Evangelizers don't say something.