TEN COMMANDMENTS of God or NEW Covenant?

Do we follow the Ten Commandments of God or the New Covenant? Some advocates of the Torah claim that the only reason some Christians reject the Old Testament is because they do not want to keep the Sabbath.

They claim there was no difference between the Old and the New Covenant. Jeremiah 31:31-34 and Hebrews 8:6-13 teaches that the New Covenant is different from the Old. It is not the same covenant at that which was delivered to Moses.