What caused the downfall of Oedipus in Oedipus the King, pride or anger?
The downfall of the protagonist of a tragedy is usually caused by the character's "tragic flaw". This is true of Oedipus as much as it is true of any other tragic figure of antiquity. Of your two choices, pride or anger, it is pride that comes nearest to identifying the tragic flaw of this character.
The ultimate cause of Oedipus' downfall is his unwillingness to accept his fate. He cannot accept the predictions about his life (that he will murder his father and sleep with his mother) and he fights against them.
Oedipus struggles against the oracle that predicts his hand in his father's death...
To do so, Oedipus must reject the very idea of fate and the idea that the gods are in control of the lives of mortals. This rejection can be seen as evidence of his great pride.
Additionally, Oedipus invites information, however damaging it might be, saying that he can handle any truth that comes his way. This also suggests a vanity and pride on his part and, ultimately, leads to his tragedy. Though his wife and others try to convince him to stop his investigation, Oedipus continues and is destroyed by his discovery:
by demanding that others tell him all they know he is forced to confront the hideous facts of his patricide and incest.
I agree with the other commenter that it is, ultimately, Oedipus's pride that is responsible for his downfall. Anger is a tempting answer because Oedipus does get so angry at Teiresias, at his brother in law, Creon, even at Jocasta, his wife and mother. However, Oedipus's anger, if we trace it, stems from his pride. He originally kills Laius on the road, in anger. But why was he angry? Because Laius and his retinue attacked Oedipus, insulting his pride.
Why does he get so angry at Teiresias, the prophet? Because Teiresias claims that Oedipus doesn't really want to know the truth, that it would be better for Oedipus to remain in the dark. When Teiresias insists that he knows better than Oedipus what is best, he wounds the king's pride. Oedipus then assumes that Teiresias must be working with Creon in order to take his crown. The idea that his brother in law believes that he is not a sound or deserving ruler (totally made up in Oedipus's own head) wounds his pride, and he becomes angry.
Oedipus makes some errors in judgment as a result of his tragic flaw, pride, and one of these errors is his quickness to become angry when someone says something he doesn't like.