Big disagreement on the issue of "just how new was the New Covenant"
Exactly! Presbyterian covenant theology treats the new covenant as a 'renewed' version of the old covenant; particularly that baptism in the new covenant is simply the equivalent of circumcision and therefore applicable for children. This is crazy for all sorts of reasons, not least that the Bible tells us that the new covenant is 'not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt' (Jer. 31:32; Heb. 8:9).
While most paedobaptists spoke of the covenants being largely the same, the early Particular Baptists stressed the difference between them, and were given a huge boost when Congregationalist John Owen, in his massive commentary on Hebrews, revealed 17 differences between the two covenants.
I think I can do no better than to list these differences, trying to put them very briefly in my own words. [I shall refer to the Sinaitic covenant as the ‘first’ covenant because that is how the writer to the Hebrews speaks of it]
1. They differ in the time of their establishment. The first was established in the third month after the coming out from Egypt of the Israelites (Exod 19:1). The second, ‘At just the right time’ (Rom 5:6, NIV); ‘In the dispensation of the fullness of time’ (Eph 1:10). ‘When the fullness of the time was come’ (Gal 4:4). ‘When the Day of Pentecost had fully come….’ (Acts 2:1).
2. They differ in the place of their establishment. The first covenant, in Sinai; the new covenant, in Jerusalem; but in this connection it is worth reading Gal 4:24-26. Sinai represents bondage; the new Jerusalem represents freedom.
3. They differ in the manner of their promulgation (Heb 12:18-26). The first came with fire and the sound of a trumpet (Exod 19:18f); the New came with a voice from heaven (Psalm 110:4; Matt 3:17).
4. They differ in their mediators. In the first covenant , it was Moses, who was faithful as a servant (Heb 3:5); in the New, it was Christ, a Son over His own house (Heb 3:6; 2Tim 2:5).
5. They differ in their subject matter. The first covenant revived the demands of the covenant of works with Moses saying, “Cursed is the one who does not confirm all the words of this law” (Deut 27:26). In the new covenant, God’s law is written on our hearts with Christ saying, “My yoke is easy and My burden is light” (Matt 11:30), and we find ourselves saying, ‘His commandments are not grievous’ (1John 5:3, A.V.).
6. They differ in the manner of their dedication. In the first covenant, it was by the sacrifice of beasts and the blood sprinkled around the altar (Lev 8, 9). The New was confirmed by the sacrifice and blood of Christ Himself (Heb 10:19-23; 12:24).
7. They differ in respect of the Priesthood. In the first covenant, the Priesthood was limited to Aaron and his posterity; in the New, Christ has an unchangeable priesthood in the power of an endless life (Heb 7:11-28).
8. They differ in the matter of their sacrifices and their access to God. The Aaronic high priest could enter in to the Holist Place only once a year having sacrificed for his own sins as well as those of the people; our Great High Priest had no sins of His own to atone for, but, ‘Not with the blood of goats and calves, but with His own blood He entered the Most Holy Place once for all, having obtained eternal redemption’ (Heb 9:12).
9. They differ in the matter of their writing down. The first covenant was written on ‘tablets of stone,’ the New on ‘tablets of flesh, that is, of the heart’ (2Cor 3:3).
10. They differ as to their purposes. ‘The principal end of the first covenant was to discover sin, to condemn it and to set bounds to it’ (John Owen; cf. Gal 3:19). The purpose of the new covenant is to show forth God’s justice and mercy (Rom 3:26).
11. They differ in their effects. The first covenant was a ‘ministry of death’ and ‘of condemnation’ (2Cor 3:7, 9); the New gives liberty (2Cor 3:17-18).
12. They differ in the grant of the Holy Spirit. It appears that during the period of the first covenant, the Holy Spirit was indeed active, but there was so much a wide and greater effusion of His power at Pentecost, that John speaks sometimes as if He had not come before (John 7:39; 15:26 etc.).
13. They differ in the declaration made in them of the kingdom of God. The term ‘kingdom of heaven’ or ‘kingdom of God’ does not appear in the O.T. Israel under the first covenant had the appearance of a kingdom of the world (physical borders, an army, a physical temple). The kingdom of God has none of these things. The Lord Jesus declared, “My kingdom is not of this world’ (John 18:26). His subjects are spread throughout the earth, and have their citizenship in heaven.
14. They differ in their substance and end. The first covenant was typical, shadowy and removable. The new covenant is substantial and permanent as containing the Body, which is Christ.
15. They differ in the extent of their ministration. The first covenant was largely confined to Israel after the flesh, with darkness reigning all around. In the new covenant, we read, ‘The people walking in darkness have seen a great light’ (Isaiah 9:2).
16. They differ in efficacy. The first covenant ‘made nothing perfect’ (Heb 7:19; cf. 8:7). It gave outward commands without giving the power to perform them (cf. Acts 15:10). In the new covenant, ‘says the Lord, “I will put My laws in their mind and write them on their hearts”’ (Heb 8:10).
17. They differ in their duration. One was to be removed; one to abide forever (Heb 10:8-9).
We see therefore that the new covenant is the outworking of all God’s plans and promises, which are seen to be ‘Yes and Amen in Christ Jesus’ (2Cor 1:20). The new covenant is in Christ’s blood (Luke 22:20) and cannot possibly fail (cf. Isaiah 42:4). It was planned and arranged in eternity, so that it is called the ‘everlasting covenant’ (Heb 13:20-21 etc.), and Christ, ‘The Lamb slain from the foundation of the world’ (Rev 13:8). It is the consummation of all the covenants of promise (eg. John 8:56; Acts 2:30), and ‘the end of the law (that is, its purpose and fulfillment) for righteousness to everyone who believes’ (Rom 10:40).