The contrast between the two passages is certainly quite notable.

Some commentators have proposed that the two writers were actually saying the same thing, if we simply recognize that Matthew was attributing the action to the person making the decision, without making reference to the intermediaries who carried out that decision. They suggest the flogging of Jesus as a parallel: “So [Pilate] released Barabbas, and after flogging Jesus he handed him over to be crucified” (Matthew 27:26); “Then Pilate took Jesus and scourged him” (John 19:1). Both of these sentences say Pilate did it, yet everyone supposes it means ‘Pilate ordered it done,’ with some unnamed soldiers carrying out the task rather than Pilate wielding the whip himself. Indeed, several English translations have actually rendered the Greek words as “Pilate had him flogged.”

The proposed explanation does have a certain attraction to it, and yet it is not entirely successful. We may well think it obvious that Pilate would not have administered the whipping himself, and therefore conclude that it is equally obvious that there must have been intermediaries who did what he wanted. But the existence of intermediaries is not at all obvious in Matthew 8.

No one reading Matthew’s text would imagine that the conversation between the centurion and Jesus was actually a series of messages carried by people running back and forth, because the centurion was still at home. If we are nevertheless supposed to understand that Matthew really meant the same thing as Luke, we have made the two writers agree about what happened – but at the cost of eroding our confidence that we can learn what Matthew meant by reading what he wrote. That’s a pretty high price to pay.

Rather than trying to demonstrate that the two passages say the same thing, it seems wiser to me simply to admit that they disagree. Perhaps Matthew consciously contracted the events, valuing brevity over detail, as preachers sometimes do; or perhaps this was simply the way he remembered it happening. Perhaps Luke consciously expanded the events, valuing storytelling over terseness, as preachers sometimes do; or perhaps this was simply the way he heard it originally. We don’t know more than that; so we should be content not to claim more than that.