I'm not a specialist on the Caesarian period (I'm much more familiar with the Late Roman Empire), but I'll give it a shot.

First, we will need to disentangle two different parts of the story: the reception of Julius Caesar in the ancient world itself, and his reception in the modern period.

First, the Roman period:

We must not forget that Caesar was often considered to be the first emperor (differing from our modern notion of what constitutes an emperor). For example, Suetonius' biography 'The Twelve Caesars' written in 121 AD starts with Julius Caesar and ends with Domitian.

To put this into context, you need to understand that Augustus didn't really 'establish the Empire' in any official sense of the modern word "Empire". Rather, scholars describe Augustus' political system as the 'Principate', meaning Augustus managed to hoard together a bunch of different powers and offices, one of which was that of 'Princeps ('first citizen'), hence the name Principate. Erich Gruen writes that:

"[T]he notion of principatus as designating a type of regime is not to be found in Augustus’ autobiographical memoir, the Res Gestae, nor in the works of contemporary writers." [1]. In other words, in the eyes of contemporaries, Augustus was not viewed as the first Emperor. With the benefit of hindsight and modern scholarly methodology, we may recognise Augustus' rule as more transformative than Caesar's, but that doesn't mean contemporaries saw it as such. After all, the establishment of a dynastic, monarchical rule was a slow process that went even beyond Augustus' lifetime, but started with Caesar.

Thus, the person of Caesar was foundational for the legitimacy of Augustus and all subsequent emperors. The Julio-Claudian dynasty traced its lineage back to Caesar and afterwards, this tradition stuck around, with the Vespasians claiming dynastic continuity with Caesar as well [2]. As is well known, Caesar was a title worn by all emperors into the Late Roman period.

By Late Antiquity, Caesar's fame had not diminished. In the preface of a law issued by Emperor Justinian in 537, Caesar is seen almost as one of the mythical kings of Rome, used to buttress the imperial legitimacy of his own regime [3]. So, briefly, we may conclude that Caesar was seen as the bedrock of imperial legitimacy throughout the Empire.

Then, the modern period.

I'm not a specialist here, and others may come with far more complete answers than I can provide. But I suspect the modern popularity of Caesar originates in the corpus of classical texts. Texts from the so called 'Golden Age of Latin literature' (ca. 70 BC - 14 AD) have the most prestige and have been studied for centuries as the epitome of western civilisation. Still today, most learners of the Latin language will start reading texts from this period.

The story of Caesar is well-documented by the literature of this period, not least by himself (Commentarii De Bello Gallico and Commentarii De Bello Civili). Caesar was therefore a popular figure during the Renaissance, written about by famous writers such as Shakespeare and Machiavelli. Augustus, by contrast, has no real literary texts of his own*, and is only more fully described by authors from the so called Latin Silver Age (e.g. Suetonius, Tacitus).

*Augustus has written a sort of auto-biography, called the Res Gestae divi Augustus (simply, 'The Deeds of the Divine Augustus') but they were written on inscriptions, not preserved in a manuscript.

Furthermore, Caesar's life has many literary qualities to it, and he is often seen as a shining example of the statesman and the general. Consider the following praising words by Theodor Mommsen, the greatest Roman historian of the 19th century:

"Caesar is the perfect man [...] a born ruler, he reigned the moods of people as the clouds obey the wind, and compelled the most different kind of people to listen to him, from the simple citizen to the rough officer, the noble ladies of Rome and the beautiful queens of Egypt and Mauritania, to the shining cavalry officer and the calculating banker" [4]

In the modern time, I suspect that the romantic story of the fall of the Republic, but also Caesar's adventures in Gaul and Egypt, simply resonate with a modern audience. Essentially, the biography of Julius Caesar simply makes for a good story. And finally, not to forget, I also imagine that the comic book series of Asterix and Obelix play no small part in the modern fame of Caesar.

Literature:[1] Erich Gruen, 'Augustus and the Making of the Principate', The Cambridge Companion to the Age of Augustus, p. 34[2] Olivier Hekster, Emperors and Ancestors: Roman Rulers and the Constraints of Tradition (Oxford 2015)[3] M. Maas, 'Roman History and Christian Ideology in Justinianic Reform Legislation', Dumbarton Oaks Papers 40 (1986) p. 17-31.[4] Translated from German, found in Viktor Pöschl, 'Caesar, Wandel einer Gestalt', Antike und Abendland 33.2 (1987) p. 172.