How do Antigone and Lysistrata compare? How are they different? How are they unique in a time when women were tradtionally "seen and not heard?"
Antigone and Lysistrata belong to two different genres. Antigone is a tragedy and Lysistrata a comedy.
Both plays would have been performed by three actors and a chorus, all male. The three male actors would have played all the roles in both plays, both male and female, changing costumes and masks to play different characters. Structurally, both plays would have been performed in the same theaters and consisted of alternating choral odes, during which the chorus would sing and dance, and episodes, in which individual actors would talk.
In the case of Antigone, we see a moral dilemma, in which duty to the gods and duty to the state are in conflict. The traditional role of women emphasized subordination and obedience to men, first fathers (or other male relatives) and then husbands. However, women also had a traditional responsibility for burial and mourning. Thus the two sisters are torn between those two duties, with Ismene representing the duty of obedience to male relatives and Antigone the duty of obedience to the gods via ritual performance. Reading this from a feminist perspective as a play about female independence is probably anachronistic.
Lysistrata is a comedy. That means that many of the costumes would include huge red leather phalluses. Although Aristophanes uses the comedy as a vehicle in which to express serious opinions about the war, the sex strike is mainly an occasion for very crude jokes, both verbal and visual, about sexual desire, and especially about male erections. The prominence of women in the play is not some sort of proto-feminism but rather something outrageous and improbable done for comic effect. Saying that even women can see the common sense in making peace is intended as a rebuke to men.
Both women find themselves dealing with the folly of men. Antigone has to overcome the overweening pride and vanity of her wicked uncle, Creon. Lysistrata, for her part, tries to knock some sense into men and make them aware of the horrors of war. Both women dare to challenge male domination in service of a higher cause. Although, there is still a slight difference between the two. Antigone believes herself to be justified in defying Creon, because it is the gods' will that she should do so. Her concern to do honor to her dead brother is inextricably linked with her reverence for the gods, so it is impossible to say whether she would've defied her uncle had she not felt that the gods were on her side.
Antigone's act of defiance is an individual one, an act of rebellion. It is Creon who has subverted the established social norms, not her. In that sense, she can be seen as attempting to restore the traditional values undermined by the king. Lysistrata, however, is boldly challenging society and the gender relations on which it is founded. Women in ancient Athens were supposed to be meek, demure, and submissive to their menfolk. Their sole province was the home and distaff. So it's considered an outrage when Lysistrata leads the women of Athens in withholding sex until the war is brought to an end. In an even greater act of subversion, the women seize the treasury to prevent any more of the city's wealth being wasted on an increasingly bloody and pointless conflict.
These two plays are alike in that strong women speak up in an attempt to control the outcomes of unpleasant situations. In Antigone's case, she is unhappy with the decree that her loved one will not be given an acceptable burial. Against the law, she buries him and faces death and the title of "traitor".
The women in Lysistrata are unhappy that their men are wrapped up in a war that seems to never end. Therefore, they get together (the women from both sides of the fray) and decide to withhold sexual pleasure from their men until the men declare an end to the fighting.
Both plays are written in a time when women were not given many rights and were expected to be "arm candy" only--lovely to look upon, silent, and obedient. It is unusual that these women would all take such strong stands in the man's world which they live.
They are unalike in the way that they flex their womanly muscles. Antigone never hinted at sex as a way to solve the problem she faced--it was more logic and character appeals that she uses to convince Creon to change his mind.