In some ways, Creon is a foil to Oedipus, showing a sense of justice and compassion that Oedipus does not. We have evidence of Creon’s lack of ambition for kingship, and willingness to compromise only from his own speeches though.
Oedipus’ downfall is that when in power, he becomes arrogant, treating Tireisias in a high-handed manner, and suspecting Creon of being after the rulership of the city rather than merely concerned about the city’s welfare. Creon claims to be concerned only for the city, and appears more pious than Oedipus and more concerned with making sure that Thebes is not offending the gods.
In Scene I, Tiresias describes Oedipus in this way:
"When it comes to speech, your own is neither temperate/
Nor opportune. I wish to be more prudent."
In these lines we can see one way to distinguish between Oedipus and Creon, as Oedipus is rash, insistent and insensitive while Creon conducts himself with some prudence and temperance.
Oedipus consistently demands to have his desires met, even against the counsel of the people that he seeks out expressly for advice and information. To say that Oedipus is "head strong" is something of an understatement.
In ways that are conceptually and symbolically significant, we can say that Creon maintains some vision - - some desire and ability to see circumstances clearly - - while Oedipus is blind hopelessly.
Even in the end, Oedipus drives forward without pausing to ascertain his options. Just as he was incapable of realizing (seeing) his role in the death of Laios and unable to recognize Iocaste as his own mother, Oedipus remains incapable or unwilling to fully look at his situation. He instead demands to be driven out of Thebes and puts out his eyes.
Creon urges restraint. Oedipus insists that "the parricide must be destroyed," but Creon advises that they hold off and really look at the situation.
"That is the sense of it, yes; but as things are,/
We had best discover clearly what is to be done."
The capacity of vision is, in one way, the decisive difference between these two characters. When Oedipus puts his own eyes out, he is symbolically acknowledging the blindness that has defined his character throughout the play.
Notably, Sophocles' Oedipus trilogy ends with Creon taking on the same kind of blindness that Oedipus displays here in the first play of the series. The kingship, it would seem, presents moral dangers that quickly become profound spiritual dangers in the Greek context. Believing oneself to be endowed with great power can blind one to the idea that the gods remain still more powerful and always ready to show that power and humble a king.
Unlike Creon, who is portrayed as the king's loyal right hand man, Oedipus is shown to be ill-tempered, vain, and brash. Upon gaining the information regarding his history and the role he played in the death of King Laius, he flies into a rage, accuses both Teiresias and Creon of lying and speaks forcefully to Creon. When Creon shows up to get to the bottom of the rumors he's been hearing regarding the accusations made against him, the chorus says, "Perhaps it was a sudden gust of anger/ that forced that insult from him, and no judgment" (8). That the chorus suggests Oedipus has spoken from anger implies that he is in the habit of doing so, and is likely known for having a temper. Creon, on the other hand, is rational throughout his entire conversation with Oedipus and questions him calmly and pragmatically to prove to him that he is innocent. Unlike Oedipus, who thinks highly of himself and his power as king, Creon has no wish to be in such a position of power and tells Oedipus this flat out. As Oedipus' brother-in-law, he has all the perks that come with being king, only without the pressures of the job.
In the second and third play, we see how similar the two characters actually are. By the time we reach Antigone, Creon has become just as power hungry and determined to remain in a position of power as Oedipus was. Creon also shows he is willing to sacrifice his own family for his power (although, unlike Oedipus, Creon does so knowingly) by ordering Antigone, his niece and future daughter-in-law, to her death. This brings on the death of his son and wife. By the end of the last play, Creon has been reduced to much the same place as Oedipus.