No lasting separate church came out of these forty years, and for that reason the Western Schism gets less attention than the division with the East. Its effects on the Latin church were nonetheless deep and long.
It damaged the papal office in a way argument alone could not have done. For two generations, obedience to a pope was visibly a matter of which king one lived under, and the claim that submission to the Roman pontiff was necessary for salvation was hard to sustain when devout people could not establish who that pontiff was. Both sides excommunicated the other's adherents, which meant most of Latin Christendom was excommunicate by somebody.
It made the conciliar movement plausible. If only a pope can judge a pope, and no one can say who the pope is, then either the situation is insoluble or some other authority in the church can act. Constance acted on the second answer, and the decree Haec Sancta stated it as a principle. Later popes rejected the principle while owing their own legitimacy to the council that applied it, a difficulty Catholic canonists have never entirely resolved.
And it left a habit of reform demands that the papacy answered slowly. The council's own decree providing for regular future councils lapsed within decades, and the grievances aired at Constance were still being aired a century later, when the answer was no longer a council.