King Edward of England contrasts with Macbeth most significantly in his ability to heal the sick, something that, for Christians, only God can do. Malcolm tells Macduff that Edward's ability is "miraculous," that he is visited by extremely sick people who are "All swoll'n and ulcerous" and whom medicine has not helped (4.3.169, 173). Edward prays for them and hangs a "golden stamp about their necks," and they are, miraculously, healed of their terrible malady (4.3.175). Further, in addition to this apparently divine gift of healing, Edward "hath a heavenly gift of prophecy" as well, and these kingly gifts have benefited the kingdom of England greatly under Edward's rule (4.3.179).
It seems, then, that King Edward is truly anointed by God, as he is able to perform miracles, such as healing the sick, and predict the future. Macbeth, of course, has no such abilities. In fact, Scotland has languished and suffered under his rule. Edward has healed where Macbeth has destroyed.
One major reason why this is important in the play is that it gives King Edward and his army license, the seemingly divine right, to invade Scotland and kill Macbeth, who is now king. At the time Shakespeare wrote the play, true kings were believed to be chosen and blessed by God, and so it was a tricky thing to consider killing a monarch. In contrasting Edward with Macbeth, Shakespeare makes it clear that, in the play at least, God was not with Macbeth, because if God were, then Macbeth would have these divine powers that Edward enjoys.