The Law of God is the same in both the Old and the New Covenants. The difference is the method used to keep them (relying on self or the power of the Spirit) and to atone for breaking them (animal sacrifices and earthly priests or Jesus).
The people made the promises in the Old Covenant, but God makes the promises in the New Covenant. This is truly great news! If we let Him, God writes the law on our hearts, which enables us to WANT to obey His laws.