The most lasting part of the rule of Constantine was that the old religion of Rome was discontinued in favor of Christianity by the state and Constantine was also converted to Christianity.
This is because of the enormous spread of the religion throughout the region and it had also made possible the level of permeation that was happening of the religion in dictating the state and how the state is functioned.
This is not something that the pagans before were doing but it certainly was what happened in early Christianity.