"[...] the ministry of the righteousness exceeds in glory far more than the ministry of condemnation..."
Paul does this comparison to speak of the failure of the ministration of self-righteousness which is about man deriving his merits by respecting the law.
The law can be summarized as any action to derive any merit on your own capacity. God used the Mosaic dispensation to show the ineffectiveness of our self-performances. The do to be paradigm is the glory that fades, forit does not produce what gives life. When you try to use your own effort, you will continually try to become but without becoming.
God INTRODUCES another ministry whereby we no longer live from the things that we ought to observe outwardly but from what we have IN US which is life. The ministration of righteousness exceeds in glory because it is the ministration of life. It transforms, generates life. It is only the Spirit that gives life. The blessing that we receive from Christ is the blessing of life. That blessing is meant to propagate and extend life.
Hearing "thou shall not” has never transformed lives but knowing that you are saved by GRACE through Christ Jesus, renews your mind.