It is noteworthy that the disagreements between Brutus and Cassius do not begin until after they have assassinated Caesar. Then almost immediately the differences in their characters and in their mental processes become apparent. What has happened is that Cassius has miscalculated in persuading Brutus to become the head of the assassination plot which he himself was organizing. Cassius knows that Brutus has far more prestige than himself. He goes to extreme lengths, including outright deception, to win Brutus over to his cause. But once Brutus has taken the leadership he is not willing to give it up.
Cassius himself is not well liked because he is not a likable man. He is greedy, selfish, miserly, envious, cunning, and treacherous. Caesar himself says of him:
Yon Cassius has a lean and hungry look.
He thinks too much. Such men are dangerous.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Seldom he smiles, and smiles in such a sort
As if he mocked himself, and scorned his spirit
That could be moved to smile at anything.
Such men as he be never at heart's ease
Whiles they behold a greater than themselves,
And therefore are they very dangerous.
Brutus, by contrast, is admired by everyone because his noble character is apparent in his features, manners, and voice. He has one fault, however; he is an egotist. This is due to the fact that he is a reclusive, studious introvert, and introverts have a strong tendency to think their inner world is the real world. Notice how he mainly talks about himself in his oration at Caesar's funeral:
...hear me for my cause, and be silent that you may hear. Believe me for mine honor, and have respect to mine honor that you may believe.
Brutus assumes he knows more than any of the other conspirators, and this is reinforced by the fact that they unanimously choose him to be their leader. They all meet at his house, not at that of Cassius. (This is just as well with Cassius because he would not like to have to provide the refreshments. His prime character trait is that he is a selfish miser.)
With everybody listening to Brutus and kowtowing to him, he becomes more and more like Caesar, the man they all want to displace. This always happens when a power vacuum is created. But the power vacuum will ultimately be filled by Antony and Octavius instead--and then finally by Octavius alone.
Cassius and Brutus disagree about allowing Antony to speak at Caesar's funeral. They have a violent disagreement in Brutus' tent. They disagree about the strategic practicality of fightinig Antony and Octavius at Philippi. Cassius is always overruled because Brutus is so egotistical, has become so convinced of his mission to save Rome, and is so much better liked and more respected than his partner. Cassius must have thought he could use Brutus as a figurehead and be the real power himself, but he misunderstood how Brutus would grow once Caesar was eliminated.
Actually, all of the principal characters grow when the number-one man is erased. They might be compared to bushes that flourish when a tree which has been monopolizing the sunlight is cut down. Even the callow young Octavius starts acting like a fierce soldier and future emperor. Cassius becomes more avaricious and power-hungry. Antony becomes more statesmanlike and less of a "masquer and a reveler." Brutus becomes more self-assured, self-important, imperious. He realizes that he doesn't need Cassius at all, but Cassius is nothing without him.