Officially Christianity is based on the 10 commandments, however, those commandments were given by the Lord to the Jewish people, so it technically has nothing to do with anyone else other than the jewish people. that information itself destroys the entire concept of the Christian faith, however; the Jewish faith has the Ten Commandments and has 613 laws +6 rabbinical laws and many more customs and precautions to protect the laws of the bible.
Another Point is: Judaism has never went on a crusade to try and force other ‘faiths’ or other people to join their faith. but we do recommend the 7 laws of Noah for all mankind as a way to encourage the people of the world to be righteous Gentiles, in essence, if you see the Bible you will see that the Ten Commandments - as well as the entire Bible - belongs to the Jews and is for the Jews.
However, Adam - the first man - was not Jewish, he got six laws then after the flood Noah - the only righteous man - on earth - received an additional law which became the seven laws of Noah that G-d gave to mankind, these laws are basic laws such as; do not kill, do not steal, do not curse G-d, respect family life establish courts of justice... and they are a good preparation - in our generation - for all mankind to be able to greet and accept the king moshiach /messiah properly.
regarding moshiach/messiah himself obviously jewish law is the only true authority that establishes such a status (see my other notes for more) and the Rebbe of chabad is the king moshiach for the entire world.