In Act 4 of Julius Caesar, what conflict between Brutus and Cassius is revealed?
In 4.3, Brutus and Cassius argue in Brutus's tent, so that their armies will not perceive discord between the two leaders. Essentially, Cassius is angry because Brutus has publicly disgraced Lucius Pella (Brutus claims Pella took bribes), despite the fact that Cassius had attempted to intercede on Pella's behalf.
In response, Brutus accuses Cassius of being greedy himself:
Let me tell you, Cassius, you yourself
Are much condemned to have an itching palm
To sell and mart your offices for gold
Later, during the same argument, Cassius claims that he is "older in practice, abler than yourself / To make conditions." Brutus, offended by this claim, misinterprets this statement and thinks that Cassius has claimed to be a better soldier than Brutus.
After some time, Brutus finally reveals that his wife, Portia, has committed suicide. (She is also Cassius's sister, making Brutus and Cassius brothers-in-law.) Obviously, the news of his wife's death has upset Brutus, making him more likely to argue. Further, the stress of the situation Brutus and Cassius are in weighs heavily on each man's mind. Ultimately, the two reconcile and vow to continue their fight for Rome.
(It is also important to note that Brutus and Cassius disagree with regard to battle strategy at the end of 4.3. Brutus feels the best strategy would be to meet the enemy at Philippi, whereas Cassius thinks it would be better to allow the armies to rest and wait for the enemies to come to them. Ultimately, though Cassius agrees to yield to Brutus, audiences learn, once again, that Cassius's wisdom and ideas would have worked out better.)