Shakespeare shows Brutus as calm, logical, poised, and magnanimous. He shows Cassius as greedy, selfish, deceitful and inclined to be a bully. The audience's sympathies would naturally be with Brutus during this argument, especially when Cassius threatens him:
You know that you are Brutus who speaks this,
Or, by the gods, this speech were else your last.
Urge me no more, I shall forget myself,
Have mind upon your health. Tempt me no farther.
Cassius reveals his true nature in this quarrel, and the audience is glad to see him defeated and humiliated by a better man.
An interesting example of Cassius's greedy nature occurs after the quarrel when Brutus orders wine for both of them to pledge their reconciliation. Cassius says: "My heart is thirsty for that noble pledge. / Fill, Lucius, till the wine o'erswell the cup. / I cannot drink too much of Brutus' love." Cassius is a miser. He cannot drink too much wine when somebody else is providing it-- and when the wine is probably of much better quality than Cassius is used to buying for himself and his household.