Do the texts of Oedipus the King and Macbeth emphasize similar things?
I think that by "similar things" the question is referring to anything from themes to the actual story plot, I have a few ideas but I'm not entirely sure.
First, they are both classical Tragedies. The definition of a what makes a play a Tragedy was coined by Aristotle in his Poetics. In essence, it must contain heightened language (ie -- be written in verse), and the plot must follow the tragic demise of its main character (or tragic hero) due to this hero's tragic flaw. The events of the Tragedy must inspire pity and fear in the audience, which basically means that the audience must empathize with the hero's fall from his high position.
Both Oedipus and Macbeth are the aforementioned tragic heroes. They both begin the play as noble and high-born men, and both "win" the kingship that they hold throughout the plays by murdering the king that preceded them. The difference is that Oedipus doesn't know that he has murdered Laius and Macbeth makes a conscious choice to murder Duncan.
Both kings have wives who die as a result of the weight of the guilt of their (knowing or unknowing) complicity in their husbands actions.
Both Macbeth and Oedipus have a moment, near or at the end of each play when they become aware of the consequences of their actions. For Macbeth, this awareness comes in his famous soliloquy from Act V, scene v, which begins with the line "She should have died hereafter." Though this line refers to the death of his queen, in the body of the speech Macbeth becomes aware that he has created a life that adds up to nothing. He has acted in order to gain everything and found that the power and prestige amounts, after all to nothing. Oedipus also has a moment of awareness at the end of the play in which he blinds himself because he believes that he no longer deserves to see the beauty of the world.
So, the Tragedies Macbeth and Oedipus Rex (or the King) share many similarities, some of which I have given above. Please follow the links below to the study guides on Poetics, Macbeth and Oedipus Rex for more information.