Explanation: Gaius Julius Caesar, of conqueror and dictator fame, went out of his way, before, during, and after his Civil War, to treat his enemies lightly, to not pursue vendettas or vengeance, and to pardon as many of his former foes as he could. By some ancient accounts, Caesar was naturally inclined towards mercy by his personality - a trait not always highly valued by the Romans, but sometimes respected as magnanimity. However, this was also certainly a shrewd political move - Caesar removed as many pretexts for his enemies to act against him as possible. How can you call a man a tyrant who has spared you, restored your offices and honors, and continued to support your electoral runs even after you took up arms against him? Who would support you conspiring against him after that?
Unfortunately, no amount of good reputation will save you from men who want you dead, and nothing spurs an aristocracy against you like the prospect of no longer being able to lord over the poors as much as they used to. Despite Caesar being a moderate (if lifelong) reformist rather than a radical, the conservatives who had opposed him his entire career let a handful of years pass before they up and assassinated him - causing the Roman people to riot against them for killing yet another reformist politician, and the most successful and popular one of them all, leading to the assassins' downfall.
Augustus, Julius Caesar's great-nephew and adoptive son, was much less merciful. Augustus took a more 'proactive' approach to his enemies. While Augustus, always the master propagandist, was careful to acquire reasonable excuses for doing so, he ensured that anyone who opposed him in the chaotic aftermath of Julius Caesar's assassination had their 'career' cut very short. And why shouldn't he, after all? Mercy had gotten his beloved great-uncle killed, even with all the power in Rome. Better to stab than be stabbed, right?
However, Augustus also got along better with the Senatorial aristocracy, in part because he murdered or expelled a good chunk of the ones that didn't get along with him, but also in part because he sought solutions outside of the normal reformer-conservative spectrum that had dominated the politics of the Late Republic. Seemingly, the Senate didn't mind their power withering away under a domineering autocrat so long as they didn't have to share power with the poors!