away, 'tis noble.

Caesar is shrewd, cunning, cautious, secretive, watchful, selfish and calculating. Antony is notorious for his hedonism. He loves sports, drinking, eating, carousing. In Julius Caesar, Cassius calls Antony "a masker and a reveller." Antony is, as the Soothsayer tells him, a bigger and better man than Octavius Caesar in most respects. He is more courageous, a much better soldier, generous, a good friend and a passionate lover. But Caesar wins out in the end because he is a younger man, whereas Antony has passed his prime and is on a downhill course which is accelerated by his obsession with Cleopatra. Going to Egypt was probably the worst thing Antony could have chosen, because the queen and her kingdom are notorious for orgies and dissipation, the kinds of pleasures that Antony has always loved. Antony's dominant character trait is emotion; Caesar's dominant character trait is intellect. Antony relies on intuition. He is impulsive, rash, spontaneous. Caesar seems cold-blooded in comparison to Antony. Caesar really despises sensual indulgence because it interferes with his ability to reason. In all of his dialogue in the play, Caesar seems cool and self-possessed. Whatever feelings he has he keeps to himself. It is no wonder that Caesar, as the Soothsayer remarks, beats Antony at any game. Caesar is a man who "plays his cards right." 

The main theme of Antony and Cleopatra is introduced in the very first lines of the play by a minor character named Philo:

PHILO.
Nay, but this dotage of our general's
O'erflows the measure: those his goodly eyes,
That o'er the files and musters of the war
Have glow'd like plated Mars, now bend, now turn,
The office and devotion of their view
Upon a tawny front: his captain's heart,
Which in the scuffles of great fights hath burst
The buckles on his breast, reneges all temper,
And is become the bellows and the fan
To cool a gipsy's lust.

[Flourish within.]

Look where they come:
Take but good note, and you shall see in him
The triple pillar of the world transform'd
Into a strumpet's fool: behold and see.

The main theme has to do with the downfall of a famous historical figure whose fortitude and acumen are undermined by a fascinating but destructive woman who is an equally famous historical figure. Cleopatra manipulates Antony to serve her own purposes. He is totally infatuated with her. He makes fatal decisions because of her. He marries Caesar's sister Octavia in order to cement his relationship with Caesar, but then he outrages both of them by returning to Egypt and resuming his lustful and riotous behavior with Cleopatra. Antony seems to know that he is on a fatal course but is powerless to change his ways at this late stage of his life. Caesar is twenty years younger than Antony; he is on his way up, whereas Antony is obviously on his way down. 

Originally, Antony and Octavius Caesar were sharing power, with Lepidus.  When Lepidus was expelled for supposedly being disloyal, that left Antony and Caesar.  Caesar was cunning, farsighted, and manipulative.  Antony was passionate and open to manipulation.  Because of Antony’s personality, Caesar was able to defeat him.

In matters of the flesh, Antony exercised poor judgement.  His portion of the Roman holdings included Egypt, and he fell under Cleopatra’s spell.  This was difficult, because he was already married.  Then, at Caesar’s behest, he married again—to Caesar’s sister.  Both marriages caused trouble for Antony. His first wife (in the course of the play), Fulvia, tried to act against Caesar.  His second wife was Caesar’s sister, so by betraying her he was betraying Caesar.  This was not a good move.

In a conversation between Antony’s man Enobarbus and Caesar’s man Maecenas, Shakespeare addresses the problems Antony’s relationship with Cleopatra is causing.

MECAENAS

Now Antony must leave her utterly.

DOMITIUS ENOBARBUS

Never; he will not:
Age cannot wither her, nor custom stale
Her infinite variety: other women cloy
The appetites they feed: but she makes hungry
Where most she satisfies; for vilest things
Become themselves in her: that the holy priests
Bless her when she is riggish. (Act 2, Scene 2) 

The implication is that Antony is under the spell of a woman, which makes him weak in the eyes of the Romans.  Caesar uses this to discredit Antony, famously reading Antony’s will and telling the people about the Donations, a ceremony in Egypt where Antony bequeathed land to children he had with Cleopatra.  This outraged the Romans.

During the battle between Antony and Caesar, Antony was beaten soundly.  He had few men, and more deserting every day due to his erratic behavior.  Caesar had Agrippa to run his battles.  Antony was outstrategized and outnumbered. 

Antony showed his volatility when he had Caesar’s messenger whipped.  This was an egregious violation of protocol, but it also showed that he was losing control.  He even challenged Caesar to a duel.  Neither got the reaction Antony hoped.

OCTAVIUS CAESAR

He calls me boy; and chides, as he had power
To beat me out of Egypt; my messenger
He hath whipp'd with rods; dares me to personal combat,
Caesar to Antony: let the old ruffian know
I have many other ways to die; meantime
Laugh at his challenge. (Act 4, Scene 1)

Maecenas tells Caesar to pay no mind to Antony’s challenge.  They will just use his state of mind against him.  Caesar will never accept it.  He has the advantage, and everyone knows it.

Antony commits suicide because he knows that Caesar has won.  He is ruthless, and Antony is afraid of what will happen if he is captured.  He has to take the only noble act left open to him, and take his own life.  Cleopatra goads him to this, making him think that she has killed herself so that he will do it.  Later, Cleopatra kills herself after talking with Caesar and realizing she cannot seduce him like she did his (adopted) father. 

The most general theme in Antony and Cleopatra is certainly love. However, Antony, unlike Shakespeare's Romeo, is a great public figure, "the triple pillar of the world," as he is described in Philo's opening monologue. Cleopatra, of course, is also a great queen. The theme of Antony and Cleopatra can therefore be summed up as "the conflict between love and public duty" or, more dramatically, "the loss of the world for love." Antony is portrayed as easily the greatest of the Roman triumvirs. Lepidus is a fool and Octavius is an awkward boy. This means that Antony could have been master of Rome and, therefore, the world. However, he chooses his love for Cleopatra instead and expresses his choice emphatically in words that would have shocked any patriotic Roman:

Let Rome in Tiber melt, and the wide arch
Of the ranged empire fall! Here is my space.
Kingdoms are clay: our dungy earth alike
Feeds beast as man: the nobleness of life
Is to do thus [embracing]; when such a mutual pair

And such a twain can do't, in which I bind,
On pain of punishment, the world to weet
We stand up peerless.