I guess it would not be a stretch to say that Abner Snopes' form of justice is primitive, and society's is more civilized in Faulkner's "Barn Burning."
Abner's sense of justice is warped, no matter what you call it. He is not entirely unsympathetic in his quest to maintain his dignity, but he goes too far when he, himself, creates the specifics that lead to confrontations between him and those better off than him. His barn burning is a great equalizer, which has some poetic justice in it, except that he brings the problems and indignities on himself. He does this, of course, because his problem is with the system, more so than with any one individual.
Society's justice is more civilized and objective. The court, for instance, recognizes that de Spain is probably inflating the cost of the rug that gets ruined, and lowers Abner's fine accordingly. The judgment the court passes down is probably fair.
Unfortunately, primitive justice in the story is probably more effective. Abner's justice accomplishes the burning of barns, while all the courts seem to be able to do is tell Abner to get out of town.