Antony is one of the three leaders of the Roman Empire and a proven soldier. We know him from Shakespeare's Julius Caesar as a former party guy who made his soldierly fortunes at Philippi, when he bested Brutus and Cassius, Julius Caesar’s murderers. He’s regarded as a noble and formidable soldier in Rome. His presence in Egypt, however, tells us that he's neglecting his own state and shows his less noble side—the one that revels in debauchery and good times. The comparison of Antony-in-Rome with Antony-in-Egypt isn’t a set up of good versus evil; it’s just two different examples of a way a man can live his life. Hey, you know what they say: What happens in Egypt stays in Egypt.
Antony is noted for his bravery, which makes his love for Cleopatra all the more interesting. The same way that he gave himself over to his soldierly duties, he submits himself to Cleopatra, and revels in the sensuous pleasures of the Egyptian world. Antony is pretty straight up about it all and admits that he is held captive by Cleopatra’s powerful spell. Interestingly, he thinks of his situation personally, and not politically.
Antony escapes being a complete hedonist, though, because his nobility shines through in his Egyptian life. He acts graciously and nobly in his political affairs, too (when he bothers to pay them any attention): Antony greets Pompey with honesty and love; when Enobarbus turns to the other side, Antony doesn’t blame him for treachery, but instead faults himself for turning Enobarbus to that path; and when Antony thinks he’s doomed to fail in battle, he bids his men to leave him, and thanks them gratefully for their service. If that's not a benevolent leader, we don't know what is (though we certainly know what isn't).
Still, there exists another, more volatile side to Antony, which his compatriots think explains his attachment to Cleopatra. His extreme emotional swings can be seen when he resolves to kill Cleopatra, and then loves her again. Yet, he is developed as a character because he’s in touch with these feelings.
Shakespeare illustrates this best in Antony's final act. What hurts Antony deeply is the notion that he isn’t living up to his own nobility, either in politics (as he’s lost to Caesar) or in love (as he thinks Cleopatra has killed herself). As Antony dies, he wishes the world to remember him as a man who was his own conqueror. By taking his own life, Antony makes a final resolute act: his death is the final assurance that, no matter the circumstance, he was the master of his own life. He represents the tension between East and West, between Egyptian delights and Roman austerity, and between the personal desires of love and valiance. In this way, he’s a complex character.