"Emperor" is a later, English, term that does not adequately describe Augustus' position--we use it, really, simply because it's convenient. Augustus was the princeps, it just means "first head," or more idiomatically "first citizen." The term had a decidedly private aspect to it, it was originally used of the princeps senatus, the nominal "head" of the senate in the middle Republic (i.e. the dude with the greatest auctoritas, usually a celebrated consular). The senate was a body of private citizens, not elected magistrates, and they prided themselves in the dignitas of such a station, that they were able to muster such auctoritas despite not being public magistrates. The princeps senatus had long lapsed by Augustus' time, but the point of reviving the term (in a very different manner) was to point out Augustus' legally private nature. The princeps was, by his very nature, a private citizen. He held enormous legal powers, but at the inception of the Principate these were powers voluntarily (with pressure of course) voted to him extraordinarily by the senate or through laws passed in the citizen assemblies. Augustus ruled by his personal power of imperium maius (a power not possessed by any legal magistrates), his tribunician power (possessed, in the case of the princeps, by a private citizen), and otherwise simply by his enormous auctoritas. Legally speaking there was nothing in the body of Roman law that provided for such powers for any magistrate, and much less for any private citizen. Caesar, by contrast, reestablished the dictatorship, which had lapsed since the end of the Second Punic War (or rather he established a new magistracy with the same name, since both his and Sulla's dictatorships were not really the same magistracy as earlier, as they had explicit purposes and were enacted by laws passed by the comitia). His legal powers were held as a result of his magistracy, unlike Augustus' holding of private extralegal power.

Moreover, the personal powers of the princeps (originally bestowed individually, there's some debate as to when these powers became packaged as a single unit) were in fact vastly greater than Caesar's. The power of the historical dictator was not absolute, and in fact there was an attempt to turn it into a collegiate office. Caesar and Sulla both really created separate magistracies with the same name, which, while granting enormous power, had explicit purposes. This was unknown in previous dictatorships, as the historical office was an extraordinary one created by senatorial vote alone (one of the few such offices). The dictatorship historically did not hold the imperium maius, and there is no suggestion in our texts that Caesar did either. Moreover, Caesar did not hold tribunician power. Both are extremely important, those two powers alone made Augustus unimaginably more powerful than Caesar ever was. Further, Augustus and later emperors had much greater power over the magistracies than Caesar did. Caesar famously bickered with elected magistrates several times during his dictatorships, and had difficulty getting them in line, since elections continued under him. But Augustus had virtually total control over the elections and the senatorial class, which had essentially been rebuild from the ground up following decades of civil war--under Augustus the election of someone like Dolabella would have been unimaginable. Augustus' power also extended through society in ways that probably never would have even occurred to Caesar, who came to his position of primacy almost by accident and was probably more concerned with his dignitas than the idea of actually ruling anything. Under Augustus urban associations like the vici or the vigiles were codified and secured, with established structures and levels of subordination to the princeps. Imperium maius also meant that the emperors could station troops permanently in the city, and the praetorians acted in the early Principate mostly as a body intended to quell civil unrest. Such things were totally impossible under Caesar, and though his dictatorships seem very similar to the Principate at first glance, in reality they're quite different at a fundamental level