The whole point of having all of the different readings for all of the different masses on Christmas is that each Gospel gives us a different perspective on Christmas. And, taken together, they give us the whole story of Christmas.
The Gospels for the Vigil, During the Night, and At Dawn are very focused on the people and details of the Christmas story, on Mary and Joseph, angels and shepherds, etc. They are very human and very intimate in what they say and in how they say it.
The readings for During the Day have a different feel to them. They take a step back from the intimacy of the other readings, and give us the big picture of Christmas. The Old Testament reading (Isaiah) is all about God intervening, acting directly to comfort his people and to restore them.
The Gospel for During the Day (John) shows Jesus fulfilling what was foretold by Isaiah. John also shows us that the child born to poor travelers is none other than the eternal Word - that God with us is one of us.