All four Gospels have differences and no one has to decide on which is correct.
What we have to remember is that these are the memories and testimonies of three witnesses and one historian who talked to witnesses. I worked for 14 years as a police chaplain and know that when four people see the same event you have four different descriptions of that same event.
People will see something from different perspectives and also notices different things than the others. Most of their story is the same so police have to sort out the whole story from the combined reports. The same holds true for the Gospels.
Mark was likely giving what he heard Peter say in his preaching and only wrote notes on what he thought was important. Notice how short it is.
Matthew the Tax collector had a view of Jesus of a sinner converted.
Luke was a convert of Paul's missions and was a historian who went with Paul to Jerusalem and talked to people who knew Jesus and compiled a history of the Life of Jesus as a second hand account. He states this in his opening remarks.
John, who wrote later in life to a church that already knew the historical gospel, wanted to give us the spiritual side of the story. His point was that God loves us so much that he went to great lengths to let us know it and call us back to belief. John also did not seem to care about chronology.
It is also important for us to remember that even all four of them together did not tell us everything Jesus said and did.