John Chrysostom

Also, he interprets more clearly the meaning of the words, "The letter killeth," declaring it to be that which we have said above, namely, that the Law showed sin, not caused it. "Much rather doth the ministration of righteousness exceed in glory." For those Tables indeed showed the sinners and punished them, but this not only did not punish the sinners, but even made them righteous: for this did Baptism confer.

Homily 7 on 2 Corinthians ↗

Theophylact of Ohrid

Again in another way he presents the same thought. Explaining his own words, "the letter kills," he calls the law "the ministry of condemnation," as the punisher of sins, not their cause. The Gospel, however, he calls "the ministry of righteousness," because it not only frees from punishment, but also makes sinners righteous. Therefore the Gospel will possess far greater glory.

Commentary on 2 Corinthians ↗

Thomas Aquinas

Then he assigns the reason for all these when he says, For if there was glory in the dispensation of condemnation, the dispensation of justice must far exceed it in glory. This is his reasoning: Glory is owed more to justice than to condemnation, but the ministry of the New Testament is a ministry of justice, because it justifies by giving life within. The ministry of the Old Testament is a ministry of condemnation, as being its occasion: the written code kills, but the Spirit gives life. …

Commentary on 2 Corinthians ↗