In Act I, Scene II Antony is depicted as a young, vibrant, athletic man due to his participating in the Feast of Lupercal race. Antony seems carefree, but at the same time, quite loyal to Caesar. Caesar asks him to whip Calphurnia as he races and Antony obediently replies, "I shall remember. When Caesar says, 'do this,' it is performed" (lines 12-13).
Brutus is introduced as a more serious, troubled, introspective character. In the same scene, when Cassius approaches him, Brutus makes a direct reference to Antony mentioning how they are so different, "I am not gamesome. I do lack some part of the quick spirit that is in Antony. Let me not hinder, Cassius, your desires. I'll leave you" (lines 30-33). Brutus shows a lack of interest in the festivities, preferring to stay off to the side by himself rather than celebrating with the crowd. Brutus shows a lack of support for Caesar, when Cassius asks him if he wants Caesar to become King and he responds, "I would not, Cassius, yet I love him well" (line 84).
To sum it up, Antony is athletic, carefree, and loyal to Caesar, while Brutus is more sedentary, serious, and skeptical of Caesar.
The first issue you should consider here is that Shakespeare's audience would have know a great deal about Caesar, Brutus, and Antony before attending the play. Plutarch, Suetonius, and Caesar himself were staples of secondary education in this period. Thus Brutus would already have been known as an admirable moral character and exemplar of Stoicism and Antony as a luxury-loving playboy with great personal charisma.
The first thing we see here is the way Antony acts in a servile and flattering manner towards Caesar, as when he states:
When Caesar says 'do this,' it is perform'd.
Brutus, on the other hand, is portrayed as more somber and thoughtful. He contrasts himself with the popular Antony by stating:
I am not gamesome: I do lack some part
Of that quick spirit that is in Antony.
While Antony has the popular touch, mingling easily with all classes, Brutus is more serious and less outgoing. Brutus is reserved and takes time to consider all aspects of a situation while Antony is impulsive and tends to act before thinking.