Throughout 2 Cor 3:1-18 Paul contrasts the spirit of the new testament with the tables of the old testament to show that the spirit of the new testament is far better.  The Spirit of the new testament is better than the law of the old testament because the Spirit of the new testament:

Is written in your heart not in stone – 2 Cor 3:1 – to commend is “to recommend as worthy of confidence.”  Paul asked, “Do we begin again to commend ourselves [5:12]?”  He did this in 1 Cor 4:15-16, when he said, “I have begotten you through the gospel.”  See1 Cor 11:1-2.  Epistles of commendation and letters of commendation are like Acts 18:27 where Apollos was recommended to the Corinthians and Rom 16:1-2 where Paul recommended Phebe to the Romans.  2 Cor 3:2 – see 1 Cor 9:1-2, “are not ye my work in the Lord? If I be not an apostle unto others, yet doubtless I am to you.”  You’re the seal of my apostleship.  Everybody knows this about you and me, like the Thessalonians in 1 Thes 1:8.  2 Cor 3:3 – ye are the epistle of Christ ministered by us not written with ink in tables of stone [referring to the Old Testament law v.7] but written with the Spirit in tables of the heart [referring to the New Covenant in Jer 31:33].  The spirit of the New Testament is in our hearts, whereby we are changed.

Gives life not death – 2 Cor 3:4-6 – we’re trusting God through Christ because we are not sufficient [2:16].  Our sufficiency is of God [1 Cor 15:10-11].  He made us able ministers [1 Tim 1:12] of the new testament… not of the letter [Rom 7:6, the law] but of the spirit [Gal 3:2-5].  The letter killeth [Rom 4:15].  The Sprit giveth life [Rom 8:2].  The law cannot give the life that the spirit gives.

Is more glorious than the law – 2 Cor 3:7-11 – he compared the law to the spirit.  The law is the ministration of death [Rom 4:15], engraven in stones [Ex 24:12], it was glorious [Ex 24:15-18], so Israel could not behold the face of Moses [Ex 34:29-35], which glory was to be done away [Heb 8:7-9].  It is the ministration of condemnation [Rom 4:15].  The ministration of the spirit, which is the ministration of righteousness, on the other hand, is more glorious [Rom 8:17-18, 30], it exceeds in glory, the glory excelleth, it remains and the other is done away.

Is plain and understandable not vailed – 2 Cor 3:12-16 – therefore, Paul’s preaching was plain, clear and simple [Prov 8:8-9; Jn 16:25, 29-30], so they could get it.  Israel, on the other hand, doesn’t “get it” when they read the old testament.  It’s like looking at Moses with a vail on his face [v.13].  They can’t see the end of the law (that which is abolished) [Rom 10:1-4; Lk 24:25-27, 32].  Their minds are blinded [Rom 11:25]. Even when they read Moses in the synagogues [Acts 15:21] they don’t understand what they are reading [Acts 28:23-27].  When their hearts turn to the Lord the vail will be taken away [v.16; Heb 8:10-11].

Gives liberty not bondage – 2 Cor 3:17 – when you get saved, you are free [Jn 8:36] from the bondage of the law [Gal 5:1, Acts 15:8-10] through the liberty of the Holy Spirit [Gal 5:13, 18, 22-23].

Conforms you to Christ not to rules – 2 Cor 3:18 – when you get saved, it’s not like a Jew looking at the old testament and not understanding what he’s reading [Moses with a vail on his face], it’s like looking at the glory of the Lord in a mirror with an open face [4:6] so that we become the image of what we see in the glass.  This is the work of the Holy Spirit in conforming us to the image of Jesus Christ [Rom 8:29, 2 Thes 2:13-14].

Conclusion: religions today are no different than the old testament law in that they keep you in bondage to a list of rules.  JW’s, Mormons, 7th Day Adventists, Roman Catholics, etc. keep you in bondage to the law. The gospel of Jesus Christ, through the Holy Spirit, frees you from bondage and gives you life and liberty while conforming you to the image of Jesus Christ.  This the law could never do.