I can hazard an informed guess: you are right that Augustus was the more senior title. Under the Tetrarchy, the two senior emperors took the traditional title of the emperor, abbreviated to Caesar Augustus, and the junior emperors took the title Caesar. Of course, the Tetrarchy did not survive long.

However, "Caesar" as a title has slightly greater antiquity. It was first adopted by Octavian in the immediate aftermath of the civil war, along with other trappings tying him to his adoptive father, because it was politically efficacious to make the association as strong as possible in the public mind. (For example, during the war with Antony, Octavian cultivated the image of himself as "son of the deified Caesar.")

"Augustus," on the other hand, originated when the Senate voted Octavian that title during the constitutional settlements. These are all facts that can be sourced to any number of texts -- my favorite on Augustan imagery is Zanker's "Power of Images in the Age of Augustus."

Now we get into conjecture. My guess would be that the slightly greater provenance of the name "Caesar" drove its popularity. To adopt it oneself was still to act in imitation of Augustus, rather than in imitation of his successors, who adopted both titles.

I'm at a loss for why Caesar's fame would have overshadowed Augustus's in post-Roman Europe. Perhaps Suetonius is partly to blame too, for grouping Julius with the first eleven emperors in his "Lives of the Twelve Caesars."