What should I do about two close friends who are competing and exchanging bad words about each other?

Your two friends are mistaken in their unjustified quarrel and in each describing the other as "unrighteous," because this description is either an insult, and the Messenger of Allah, peace and blessings be upon him, said: "Insulting a Muslim is a Fusuq (disobedience), and fighting him is Kufr (disbelief)," or it is contempt, and the Messenger of Allah, peace and blessings be upon him, said: "It is enough evil for a Muslim man to belittle his Muslim brother," or it is backbiting, which is among the major sins. Advise your two friends to reconcile and abandon this behavior, otherwise, beware that their conduct might infect you.