Brutus' internal conflict is lead by his ultimate goal of wanting the best for Rome. He truly believes that killing Caesar was in Rome's best interest, but now that they're at war he is struggling.
This internal struggle leads to the conflict with Cassius, because he is so honest and true to his morals. He reprimands a person for taking bribes even though Cassius said it was okay. This causes them to argue, during which Brutus says "Did not great Julius bleed for justice' sake?...What, shall one of us ... Contaminate our fingers with base bribes". Brutus is angry because he truly believes they acted nobly and doesn't want Cassius to ruin that streak of what he considers justice.