John Owen lists eleven ways in which the Old and New Covenants differ.
(1) They differ in their circumstance or timing.
(2) They differ in their place—the first was declared from Mt. Sinai, the second was declared from Mt. Zion (Is. 2:3).
(3) They differ in their manner of establishment. The old came with terror. The new came with meekness and grace.
(4) They differ in their mediators. The old covenant had Moses as a mediator (Gal. 3:19). The new has Christ.
(5) They differ in their subject-matter.
(6) They differ in the way they were sanctioned—the old was sanctioned by blood from animals; the new by blood from Christ.
(7) They differ in priests—the Levites in the old, Christ in the new.
(8) They differ in the nature of the sacrifices.
(9) They differ in the way they were written. The old covenants were written in stone. The New Covenant is written in the heart of man (Jer. 31:31-34).
(10) They differ in their purposes—the old covenants imposed laws which conditioned man’s participation therein; the New Covenant gives grace sufficient for man’s inclusion.
(11) They differed in effect. The Old Covenant was a ministry of death, signed in circumcision of the flesh and animal blood (2 Cor. 3:7). The New Covenant, on the contrary, gives life and liberty to all believers.
Cf. Nehemiah Coxe & John Owen, Covenant Theology from Adam to Christ, (Palmdale: Reformed Baptist Academic Press, 2005), 200-205.