The difference can mainly be seen in Act II, scene i (Brutus and Portia) and Act II, scene ii (Caesar and Calpurnia).
Portia talks to Brutus as though she were his equal, which was uncommon at the time. Wives were barely more than property and were to obey their husbands. However, Portia calls Brutus on his behavior: he's been moody, unresponsive and is now unable to sleep and walking amid the rain in their orchard in the middle of the night. When he orders her to go to bed, and tells her he is simply ill, she refuses and tells him that he's too smart to be outside in the rain if he is ill. Portia then tries to convince Brutus to tell her what's on his mind, using guilt and trying to prove how mentally and physically strong she is. She also insists that he took her as a partner, so by the right of her position, she should know what's on his mind. We can tell by Act 2, scene iv that he does tell her.
In contrast, Caesar and Calpurnia's relationship is more typical of Roman marriages. While Caesar listens to his wife's concerns about not going out of the house that day, he ultimately makes the decision to leave the house, calling her dreams and warnings foolish. He is in charge of the relationship. In Act 1, scene i, Calpurnia's only line is "Here, my lord", showing her obedience to him.
The relationship of Brutus with Portia compared to that of Caesar's with Calphurnia is different in many directions, for Brutus and Portia have a soul-attached bond, when the conspirators went to Brutus' house to plan the purging murder, Portia was broken, and told Brutus that she can be able to handle any secret, for their vow indicates they are two halfs joined to complete one, and Brutus was indeed heartbroken to see that his wife, whom he dearly loves, kneeling and sad to hear that her husband is hiding something from her, so he did tell her his secret.
On the other hand we have Caesar and Calpurnia, when she had the nightmare and thought of it as a bad omen, she went to him in a very worried manner to tell him to listen to her, but he was too proud of himself, stating in Act ii scene ii "Cowards die many times before their deaths. The valiant never taste of death but once." secondly, Calpurnia calls Caesar "My Lord" in obedience to him, and we also see that Caesar gets ashamed of himself that he listened to Calpurnia telling him not to go to the Senate because her dream may convey a bad omen from the gods, because he listens to what Decius tells him manipulatively that her dream has been misinterpreted and the real interpretance is that the Romans happily soaking their hands in Caesar's blood means that the Roman's will nourish themselves in his power and that if he doesn't go to the senate the people (conspirators) will change their minds about giving him the crown, so Caesar believes Decius' words and gets ashamed of believing his wife's alarming worries.