There is no simple answer to this question, but I can cover one particular aspect of it (and maybe others help out).

One important factor in the transition is that Octavian, after Actium, took slow but deliberate steps to ensure that the avenues to power were cut off from future possible rivals. In the first century, the major avenue to power had been extraordinary imperium that went beyond the mos maiorum of the Republic. For instance: Marius being consul 7 times during the emergency of the invading Germanic tribes; Pompey's command against the pirates in 67 BCE (or really anything Pompey did in his whole life); Caesar with imperium for two five-year terms in Gaul; and similar years-long mandates for Antonius and Octavian. These extraordinary commands were not new -- others had held them before (like the elder Antonius against the pirates before Pompey) -- but in the 1st century BCE they became the locus of elite competition, and if you didn't attain them, you weren't in the mix to be one of the principes of the era.

After Actium, Octavian ensured that no one else would hold one of these extraordinary commands except by his permission. Agrippa had a couple, and later Drusus and Germanicus, for example, but no one from outside the circle. This cut off rivals from getting up to no good and, as a consequence, raising legions out on the frontiers to threaten the capital (exactly like Caesar had done in Gaul in the 50s). In essence, Octavian returned Rome to the days of the middle Republic, when a young aristocrat had a very proscribed path to satisfy the expectations of his relatives and ancestors. He would be a tribune, quaestor, aedile, praetor, consul, and then perhaps a proconsular governor. If he was lucky, he might become a censor at some point, or hold a prestigious priesthood. That was it. He would lead no legions unless under the watchful eye of the emperor; he could engage in public munificence, pending Imperial approval. His avenues for the accumulation of prestige were carefully regulated.

Of course, you don't just snuff out elite ambition like that. It simmered under the surface, repressed, until opportunities arose. In 69 CE, for instance, the Julio-Claudian dynasty finally faltered and almost immediately, the old ambitions surged, giving us civil war and the famous year of the four emperors. But during the long reign of Augustus, we get the sense that the Roman elite (or what was left of them) were more than happy to allow Octavian to dominate. There had been civil war and/or civil strife for decades, and we get the impression that the city was just worn out and ready for stability, which Octavian offered in a way that was no abrasive. That's a key difference between Caesar and Octavian -- Caesar had come across as an autocrat, as arrogant, and as an invader. I'm not someone that is an Augustus worshipper (like many historians are), but I grudgingly admit that he learned a valuable lesson from Caesar's behavior and was very savvy with how, and when, he asserted his authority. I think of him less as a brilliant innovator and more of a guy who knew his recent history well and who was able to take away valuable lessons from his forbears, especially Caesar, Pompey, Cinna, Sulla, and Marius.