In terms of how a Noahide Court System is supposed to function, there is an alleged malochet between the Rambam and Nachmonides. The Rambam states that the purpose of a Noahide court system (the seventh and final law for B'nai Noach being to create a court system) is exclusively to enforce the other six laws; Nachmonides gives such court systems broader powers. See below:
The Obligation to Create a System of Laws
According to the medieval philosopher and codifier Maimonides, the legal system which Noahides are required to set up is specifically to establish punishments for infractions of the other six Noahide laws (Laws of Kings 9:14).
Nahmanides, a medieval Bible commentator, understands the obligation more broadly:
In my opinion, the laws which the Noahides were to establish according to their seven commandments is not only to establish courts in each town, but that they were also commanded concerning theft, abuse, usury, labor relations, damages, loans, business, and the like, just as Israel was commanded to set up laws in these matters (Nahmanides, Commentary to Genesis 34:13).
Later authorities, including Rabbi Moses Sofer (1763-1839), claim that Maimonides did not exclude what Nahmanides had included, but that Maimonides considered all of these laws to be included under the prohibition of “theft.”