Does Sophocles favor either Antigone or Creon?

Sophocles allows both Creon and Antigone to air their views in full and the play never really leaves any room for doubt that both sides have valid claims to make. Antigone however is generally recognised as the heroine of the piece; the play after all is named for her and she appears as a figure of towering integrity and sheer courage, upholding her ideals to the death and never betraying any signs of weakness. Creon, on the other hand, comes across as something of a tyrant. Even more significantly, by the end he appears a crushed and pitiful figure as his actions lead to the suicides of his wife and son and he knows he has incurred the wrath of the gods.

From all this, it might be said that Sophocles takes the side of Antigone, but we also have to be cautious in saying this. Antigone appears just as proud and unbending as Creon and her final act of suicide, although it might be viewed as defiance, also suggests, of course, that even she has finally given way to despair. Even more important is the fact that although Creon, who opposed her views, is ultimately punished, there is no-one in the play who actually states that she was right to do what she did.

Does Sophocles take a stand in favor of either side (Antigone or Creon) in Antigone? How?

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.

In Sophocles' Antigone, whose argument is more convincing: Creon's or Antigone's?

Antigone by Sophocles is set in ancient Greece, a place known as the birthplace of democracy but a place which also reveres the gods. It is a fitting setting for this play, as the primary conflict of the play is between natural law and man's law.

Antigone argues for natural law, what she calls "the laws of the gods." She believes she must disobey the law of man if it comes into direct conflict with this higher law. For Antigone, this means that she must disobey Creon's edict and go bury her brother. She knows the consequences but feels as if her brother's eternal destiny is more important than any man-made law.

Creon, of course, argues the opposite: that the law of the land supersedes any other form of law. There is a consistency to his position, as no one will get to pick and choose the laws he (or she) will or will not obey; however, there is also a stubbornness to it which suggests that Creon simply does not want his will to be crossed.

In a perfect world, where man's law is not based on personal animosity or feelings (which seems to be at least partially the case with Polyneices), perhaps man's law could be trusted to value the right things and allow for the basic humanity of all. As it stands, however, it seems to me that natural law must be followed when man's law is wrong, weak, or warped. 

When Creon and Antigone actually face off on this issue, Antigone boldly says the following:

         Zeus did not announce those laws to me.                       And Justice living with the gods below
          sent no such laws for men. I did not think                     anything which you proclaimed strong enough
          to let a mortal override the gods
          and their unwritten and unchanging laws.
          They’re not just for today or yesterday,
          but exist forever, and no one knows
          where they first appeared. So I did not mean
          to let a fear of any human will
          lead to my punishment among the gods.
          I know all too well I’m going to die—                               how could I not?—it makes no difference                       what you decree.

Antigone's position seems stronger to me. Though she is every bit as stubborn and unyielding as Creon (they are related, after all), her motive is love for her brother and concern for his afterlife. Creon, on the other hand, just wants his word, capricious or not, to be law; that is excessive, unbending, unyielding pride. Could Antigone have gone about things differently? Of course. However, she would never have made a dent in her uncle-king's pride. I admire the fact that Antigone does not whine about the price she might have to pay; she simply knows what must be done and she does it, knowing what her actions will cost her. 

Obviously which argument is best is a personal opinion, and I would encourage you to formulate your own, based on the reading and your personal ethic. Sophocles obviously did not choose sides, as both Creon and Antigone suffer great loss for holding their positions: Antigone is dead and Creon loses everything and wishes her were dead.