The gospels are endlessly fascinating, and this is not hyperbole. John, in concluding his own gospel, writes, "there are also many other things that Jesus did; if every one of them were written down, I suppose that the world itself could not contain the books that would be written." But apparently not everything Jesus did and said was written down, because the world is not deluged with books containing the deeds of Jesus. However, we do have the four gospels, which is enough difference and puzzlement for many other kinds of books to have been written over the centuries, books on the life of Jesus and the gospels that record that life.
There are as many ways to try and compare and contrast these gospels as there are words to write about Jesus. Christians and theologians have been puzzling over the purpose of having four gospels for quite some time. Some of them have been uncomfortable with the presence of four, so they edited and combined them to form one. For one such example, take a look at the Jefferson Bible, compiled by Thomas Jefferson,http://www.angelfire.com/co/JeffersonBible/
Other scholars, discovering that more than four gospels were written in the period after Jesus death and resurrection, have drawn attention to the divergent narrative and theological elements of such writings as The Gospel of Thomas and The Gospel of Judas. Again, if these interest you, you might look at the writings of Elaine Pagels on Thomas, or Bart Ehrman on Judas.
You might know by this point, however, that although I pay attention to research into these alternative tellings of the story, I am not persuaded by them. Unlike Ehrman and Pagels, I believe that the four gospels we do have are sufficient, reliable, and together present the best composite portrait of Christ, his ministry, confession, and mission. They are our central texts for common worship. I believe we can trust that those who wrote and then later those who selected these four gospels for inclusion in the New Testament corpus did so with a good sense of the orthodox, catholic (small c), apostolic, and holy nature of these texts. If you are interested in reading on the topic of authenticity, etc., consider Richard Bauckham's Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony .
There are many ways to compare the gospels. One way to compare them is based on content and historical method. The Wikipedia article on this provides a wealth of information: http://en.wikipedia.org/wiki/Gospel
Another way to compare them is to mention the intended audience. When you write a letter or book, you have an audience in mind. You modify your style, or select the content of what you are writing, based on the audience. I think this question of audience contributes greatly to the ways each of the gospels differs. For example, the intended audience of Matthew is likely the Jewish community, so the opening genealogy of Jesus references the history of Israel. However, in Luke, a book intended for Gentile readers, the historical markers are more secular, mentioning who is governor at the time of Jesus birth.
But if we start to compare, things will get detailed very, very fast. Consider looking at this comparison chart: http://catholic-resources.org/Bible/Four_Gospel_Chart.htm Fascinating, isn't it?
I tend to think that we are called by God to allow these gospels to meld in our mind so we gain a unified biblical imagination, a composite picture of Christ and who Christ is for us. But we are also called to honor the differences between the gospels, and not prematurely meld them together, just like we are called to honor the differences between each person we meet. I encourage you as a reader of the gospels, therefore, to rejoice in and study these differences, but remember that they are each a window into and presentation of the one, whole Christ, who is our life.
The gospel writers themselves had such an intention. Again, going back to John, he says, " Now Jesus did many other signs in the presence of his disciples, which are not written in this book.
John 20:31 But these are written so that you may come to believe that Jesus is the Messiah, the Son of God, and that through believing you may have life in his name. " Or Luke, "Luke 1:1 ¶ Since many have undertaken to set down an orderly account of the events that have been fulfilled among us,
Luke 1:2 just as they were handed on to us by those who from the beginning were eyewitnesses and servants of the word,
Luke 1:3 I too decided, after investigating everything carefully from the very first, to write an orderly account for you, most excellent Theophilus,
Luke 1:4 so that you may know the truth concerning the things about which you have been instructed."