The pattern of prayer. Parallel passage: Luke 11:2-4. For most suggestive remarks on the Lord's Prayer, both generally and in its greater difficulties of detail, compare by all means Chase, 'The Lord's Prayer in the Early Church:' (Cambridge Texts and Studies).
Observe:
(a) St. Matthew's words, "Forgive us our debts," represent an older, because parabolic, form of expression than the apparently interpretative "Forgive us our sins" in St. Luke.
(b) St. Matthew's words, "as we also," seem to be expanded into "for we ourselves also," in St. Luke.
(c) St. Luke's "day by day" occurs elsewhere in the New Testament only in his writings (Luke 19:47; Acts 17:11), so that it is likely to be his own phrase, and therefore less original than St. Matthew's "this day" (cf. Weiss, 'Matthiaus-Ev.,' and Page, Expositor, III. 7.436). On the ether hand, the words, "Which art in heaven," are so characteristic of St. Matthew (Matthew 10:32, Matthew 10:33; cf. Matthew 12:50; Matthew 15:13; Matthew 18:10, Matthew 18:14, Matthew 18:19, Matthew 18:35; Matthew 23:1-39. 9), and especially of the sermon on the mount (Matthew 5:16; Matthew 6:1; Matthew 7:11, Matthew 7:21; cf. Matthew 5:45, Matthew 5:48; Matthew 6:14, Matthew 6:26, Matthew 6:32), that it seems more natural to suppose that this clause at least was added by him or by the authors of his sources to the original form, rather than that it was omitted by St. Luke. In connexion with this it may be pointed out how easy it was for our Lord to say only "Father" (Luke 11:2) immediately after his own prayer to him (Luke 11:1).
Taking everything into consideration, it seems reasonable to arrive at two conclusions. First, that the form in Luke presents, as a whole, the more primitive and original instruction of the Lord, and that that given in Matthew presents the Lord's words as fully developed, partly perhaps by himself directly, partly by his indirect guidance of Christian usage. St. Matthew's Gospel would thus at once both show the effect and be the cause of the preference for the longer form in liturgical use. Secondly, and more exactly, that both the evangelists record the prayer after it had passed through some development in different parts of the Church, St. Matthew giving it a generally later stage, but preserving one or two clauses in an earlier and better form.