Matthew and Luke - There are a number of differences between these Gospels. Matthew takes up the birth of Christ from the Father's (Joseph's) side and Luke from the Mother's (Mary's). In Scripture the male is the responsible side (God challenged Adam first in Genesis 3:9-12) and the female the supportive side (a help-mate or counterpart - Genesis 2:18). Further, Matthew in chapter 7 verses 24 to 27 speaking of two houses contrasts the materials on which they were built: rock in the one case and sand in the other. Luke in chapter 6 verses 48 & 49, on the other hand, in speaking of two houses contrasts the one built by
the man who dug and went deep with the one built by the man without a foundation. Matthew here emphasises the objective side (the material on which the house was built) and Luke the subjective (the work the man had to do). Matthew speaks much of Christ's authority (I say unto you - Matthew 5). Luke rather refers to the need for prayer (Luke 18:1) and speaks several times of Christ praying (Luke 3:21; 5:16; 6:12; 9:18, 28/29; 11:1; 22:41 & 44). There are some 13 references to prayer in Matthew's Gospel, but 23 in Luke's Gospel and 27 in Luke's Acts of the Apostles. At the end of Matthew we have the power (authority) that Christ has (Matthew 28:18), but at the end of Luke we have the power (ability) that would clothe the disciples (Luke 24:49). Matthew emphasises witness. He often speaks of twos on the same side, but Luke speaks of twos on opposite sides. For an example compare Matthew 27:44 with Luke 23:39-43.
Mark and John - Mark emphasises the Lord as a servant. There is no nativity narrative. John similarly has no nativity narrative, but speaks of Christ as the one who was before creation. Mark begins with the messenger (Mark 1:1-3), but John speaks of the Word that was with God (John 1:1-3). John speaks of the giving of Christ by God (John 3:16), his sending by him (John 4:34; 5:23 etc) and also of God as the one who has begotten those who are given the right to be children of God (those born of God - John 1:12/13; 3:3 & 3:5). It is God the Father who is behind everything in John. He is behind the work of Christ (John
4:34), his message (John 7:16/17) and the coming of souls to him (John 6:44). Mark concentrates on the things that Christ did and the happenings in the period of his service, but John gives much more in the way of dialogue.
The Four Gospels - Traditionally Matthew was written in Palestine and for the Jews (hence the many quotations from the Old Testament). Mark was written in Rome and for the Romans (the narrative is simpler and is found useful in bringing the Gospel to so-called primitive peoples today). Luke was written for Greeks and possibly in Greece (hence the recipient was one Theophilus). John was written in Asia Minor (this is in accord with the fact that in the Revelation he addresses the seven Assemblies that are in Asia - Revelation 1:4). John's Gospel is thought to have been written last and probably partly to meet
errors that were coming in among the people of God and criticisms from those without - for example, John 19:32-36.
Conclusion - The above comments are not intended to be definitive but to suggest thoughts for consideration. There are many more thoughts that can be obtained from the Gospels.