These verses proclaim another significant difference between the glory of the old covenant of law and the glory of the new covenant of grace. This difference is seen in various contrasting phrases: "was glorious" versus "more glorious," "had glory" versus "exceeds much more in glory," "made glorious" versus "glory that excels," and "was glorious" versus "much more glorious." The old covenant of law is characterized by substantial glory, whereas the new covenant of grace is characterized by excelling glory.
It is certainly true that the law is glorious. That glory pertains to the holy character of God revealed in its standards. "Sanctify yourselves therefore, and be holy, for I am the LORD your God. And you shall keep My statutes, and perform them: I am the LORD who sanctifies you." (Leviticus 20:7-8). This revelation of God's holiness in the law also exposes the unholiness of man. "Now we know that whatever the law says, it says to those who are under the law, that every mouth may be stopped, and all the world may become guilty before God" (Romans 3:19).
When a person struggles and struggles with a major medical problem, it is agonizing to go on and on, not knowing what the problem actually is. It is glorious when someone is able to reveal what the problem actually is. Part of the glory of the law is that it reveals the basic problem under which all humanity struggles: sin. Yet, it is a far more glorious matter to have a remedy for a problem revealed. Grace is that remedy. "Moreover the law entered that the offense might abound. But where sin abounded, grace abounded much more, so that as sin reigned in death, even so grace might reign through righteousness to eternal life through Jesus Christ our Lord" (Romans 5:20-21).