Aristotle in his analysis of what a tragedy is argued that a tragedy must include both a reversal and a recognition. A reversal according to Aristotle is a moment of irony when an action that it is thought will have one outcome will actually produce the opposite outcome, with tragic consequences. Recognition comes when the tragic hero has an epiphany that results in their understanding of who they are and what they have done. Aristotle believed that the climax of a tragedy came when both the reversal and the recognition collide.
In Oedipus Rex, the most important scene with regard to these concepts is when the Messenger arrives on stage as one of the last of a series of characters who provide crucial information about the murderer of Laius. What is so crucial about the Messenger however is that Oedipus hopes that the Messenger will provide conclusive proof that Oedipus has nothing to do with the death of Laius and that he has no relation to him. However, the reversal occurs when the Messenger is actually the person who identifies Oedipus as being the son of Laius:
Look, here he is, my find old friend--
the same man who was just a baby then.
This of course triggers the recognition of Oedipus as he has to confront his true identity and how he cannot avoid his fate.
In King Lear, the reversal and recognition scenes come in Act V scene 3, when Edgar sends a messenger to try and halt the execution of Cordelia. Of course, the reversal is that the messenger does not reach the captain in time, and Lear enters the stage cradling the dead body of his daughter, triggering his final and ultimate recognition of what he has done and the tragic finality of death. Note what he says as he speaks to the corpse of Cordelia, exhorting her to show some sign of life:
No, no, no life?
Why should a dog, a horse, a rat have life,
And thou no breath at all? Thou'lt come no more.
Never, never, never, never, never.
The final line of this quote has been argued to be the most tragic in all of Shakespeare, as Lear is forced to confront the fact of his daughter's death and how it can never be undone, just as his own actions and past mistakes can never be undone. The collison of reversal and acceptance make this incredibly tragic and powerful.
The original question had to be edited down. I would say that the moments of reversal in both dramas would be at the points where there is a complete change in both characters. Aristotle defines the reversal as "change by which the action veers round to its opposite." In King Lear, I think that the reversal would be when King Lear enters the storm. In Act III, scene 2, Lear faces the storm as a completely different man than he has been in the drama. From the regal monarch who believed he had the loyalty of his daughters, he enters the storm as one who would rather give into "madness than weep." Lear enters the storm only with the fool, and is apart from his royal entourage. He has become a man abandoned, with no kingdom or riches that define him any longer. His condition represents the idea of "veering round to its opposite." For Oedipus, the final act of the drama is where his reversal is most evident. From the king of Thebes who reigned supreme, he has become an object of pity. From the royal monarch who was married to the beautiful Jocasta, he has recognized that he killed his father, slept with his mother, and has committed the worst of actions. In blinding himself and seeking to wander around the countryside, his reversal is one that shows him to be vastly different than when he started. Oedipus' reversal is enhanced through the "sea of dire misfortune" in which he is immersed at the end of the drama. For both plays, these moments mark the point of reversal where "the action veers to its opposite."