That's what a pilot program will struggle to determine. Three Native American tribes, including the Pascua Yaqui here in Arizona, are being permitted to administer tribal justice a year ahead of when the overall law permitting separate courts will be enacted among the other 563 tribes in the U.S. The legal underpinnings for this include the Indian Reorganization Act of 1934. Back then Native Americans received support for establishing their own justice systems. Here is coverage of this legal development in The Washington Post.
Among members of the Pascua Yaqui, there has been the problem of domestic violence against females by spouses and boyfriends not of the tribe. Until this law, the authorities on the reservation could only encourage the alleged miscreant to get out of town. Usually that was not successful. Thanks to the law, they can now make an arrest and hold a court trial.
The pragmatists among us see immediately this can be a deterrent. Knowing arrest is possible, males might refrain from violence. And this would be a good thing. As for the issue of judicial fairness, there are so many questions. At the very least, the values of the tribal justice system could differ from those of the U.S. justice system.
Reflection: Could this be the beginning of the recognition of multiple codes of justice in America?