This difference is primarily illustrated in the first two scenes of this act. Antony has been called home from Egypt, where he has become enamored with Cleopatra. Caesar is far more concerned with the threat of Pompey, and we can see the rift beginning to widen between these two men - Antony, who has trouble governing his own self and passions, and Caesar, whose self-discipline and single-mindedness lead to his success in becoming emperor of Rome.
The links below will give you more information about these two characters, as well as the first two scenes of Act II. Good luck!