Van de Sandt, Huub. "Chapter Seven: Matthew and the Didache." in Sim, David C., and Repschinski, Boris (editors). Matthew and His Christian Contemporaries. London: T&T Clark, 2008, 123-138.
Van de Sandt recognizes a strong affinity between the Didache and Matthew's Gospel, detailing a number of the thematic similarities (Van de Sandt 2008, 123). Scholarly consensus in the past was that the Didache drew on the final form of Matthew and perhaps Luke. The line of thinking which places the Didache near the end of the first century suggests the influence of Matthew was strong at that time (Van de Sandt 2008, 124). The views which make Matthew dependent on the Didache, in Van de Sandt's opinion, push the dating of the Didache much earlier and possibly too early. However, dependence on a common tradition is quite plausible.
Both Matthew and the Didache use obedience to the principles of Torah (particularly commands to love your neighbor, fulfilling the second table of the commandments) as key to their moral code (Van de Sandt 2008, 125). The manner of interpretation is similar in each text. Van de Sandt evaluates this idea in greater depth by looking at the Didache's Two Ways section, as it provides a way of understanding matters considered those of life and death (Van de Sandt 2008, 127). The Way of Life is built on the foundation of love for neighbor. The Decalogue serves as the unifying principle for the Didache (Van de Sandt 2008, 129). Likewise, in Matthew 5, observance of righteousness is what brings perfection (Mt. 5:20-48) (Van de Sandt 2008, 130). The Didache also describes perfection in terms of obedience to commands of righteousness, first in non-retaliation (1:4) and then in obedience to all God's laws (6:2) (Van de Sandt 2008, 133).
Matthew and the Didache do not treat practical matters of carrying out the Law in the same way. Van de Sandt observes that Matthew calls for detailed observances of the Law in such a way as to go beyond the specific commands and reach for the intent or implications (Van de Sandt 2008, 135). The Didache does speak (6:2) of perfection through keeping the commandments. However, immediately afterward it relaxes the stance. This is the opposite of Matthew's view (Van de Sandt 2008, 137).
Van de Sandt concludes that both documents take Torah for granted and as a means of some sort of perfection (Van de Sandt 2008, 137-138). They have different ways of going about this quest for perfection, particularly in the case of addressing Gentiles. The Didache has a different standard. While Gentiles are to attempt to observe Torah, it is recognized as being a cultural departure for them. This is more akin to Paul's view that the law is good but not salvific.