This is an interesting question, because one could argue either side of it. The story of Antigone is part of the Oedipus cycle—she is Oedipus's daughter—and Eteocles and Polyneices were his sons. After doom comes upon Oedipus, he flees Thebes to wander the countryside as a blind beggar. The city is left without a ruler, and it plunges into civil war as Oedipus's sons fight for control of Thebes (this story is detailed in Aeschylus's play Seven Against Thebes). Antigone opens at the end of this war, when Creon, Oedipus's brother-in-law, becomes the king.

Creon leaves the body of Polyneices unburied to serve as a warning to any remaining rebels in the city: make war on Thebes, and this will be your fate. Leaving the dead unburied was a severe taboo in Ancient Greek society, as it was felt to be offensive to the gods and prevented the soul of the unburied corpse from crossing the River Acheron into the Underworld. By threatening people with the spectacle of an unburied enemy, Creon is making a powerful statement about how he intends to deal with dissent.

Antigone, Polyneices's sister, is appalled, and her outrage is the locus of action in the play: she insists on burying her brother, despite Creon's order forbidding it, and she will not be intimidated, cajoled, or threatened on this point. Creon sentences her to death for her disobedience, although in doing so, he loses his own son (Antigone's fiancé) and his wife, who both kill themselves.

So who is "right"? Which character does Sophocles "support"? Arguably, he must support Antigone, because her death is portrayed as unjust. Creon reaps terrible consequences for his actions. However, audiences at the time would have been aware of the broader context of the story and the need for a ruler to set immovable boundaries in society after a civil war. Creon is stubborn, prideful, and harsh, but he is also responsible for an entire city that has just gone through years of upheaval. Antigone's rebellion is not simply the act of a loving sister, it is a brazen defiance of orders which risks further social unrest. It is clear from the text that she is just as stubborn and proud as Creon, but because she is the eponymous victim of the play, she is more sympathetic.

I think the obvious answer is that Sophocles "favors" Antigone because her death is decried as profoundly unjust, but it would be interesting to delve into how he shows Creon's side of the disagreement and Creon's justifications for his actions.

This question is the key question of the play.  Antigone most obviously has Sophocles' sympathy, yet she is as headstrong, prideful, unwilling to compromise as her uncle.  The play is skillfully balanced.  We see Creon's need to establish order, to maintain his authority, to punish those that would bring violence to the  city-state.  But we also see Antigone's fierce loyalty to her family, her gods, her own integrity.  The chorus warns each of them about their unwillingness to bend.

At the heart of the play is a question of priorities and the consequences when priorities clash.  Neither character  is evil.  Neither is clearly wrong or clearly right. Neither will listen to the other.  Each is certain of his/her rightness.  Either course seems to exclude the other--or does it?  Is Ismene's willingness to let things be a suitable course of action?  Is Haemon's reasoned approach better?  Perhaps what should be done could be better answered by looking more closely at the minor characters and at the chorus.

It sure seems to me he does take a side.  How Sophocles chooses to characterize each of the principle players  tells me he sides with Antigone.

Ismene is weak and submissive, accepting what is without question or action. 

Antigone is strong and passionate about doing what's right, whatever the cost.

Haemon is an obedient son; however, once he recognizes his father's unwillingness to bend in the least for those who matter most to him or to see reason, he sides with Antigone.

Creon is arrogant and prideful--unwilling to bend even for his neice/future daughter-in-law and his nephew.  Ego and being right matter more to him than anything else.

In the end, all three suffer for their actions; clearly, though, the root of all these tragedies is Creon's pride.  His law (state law) is unjust in that he decrees it out of pride and personal revenge.  That tells me Antigone is on the side of righteousness, according to Sophocles, because she chooses moral law over an unjust state law. He clearly outlines the consequence of such disobedience, but he is most sympathetic, I think, to Antgone's cause.