I understand that the divide was not analogous to modern ideological politics - in the main the distinction was a stylistic one, with populares Senators relying on the plebeians for political supply and optimates preferring to appeal to established interests, but neither signifying any commitment to a broader paradigmatic worldview. Neither were the two factions parties in a modern sense, with men like Pompey floating from one camp to the other over the course of their lives.
Still, the divide was real enough to lie at the heart of Caesar's Civil War. Caesar's victory might be regarded as a victory by the forces of moderate popularism, to the extent that Caesar himself was one.
How long after Octavian ascended to the purple did this distinction remain relevant politically? Was the Empire understood in an 'ideological' sense as some kind of populares political project? Did these pre-Imperial factions continue to exist in the same way?
Well Syme didn't think them to be anything but a faction and not a significant 'political party'. He attributes it as in-fighting by the same general body: the nobiles, "as individuals or in groups, open in the elections and in the courts of law, or masked by secret intrigue".
Syme says the populares were merely the name of the people who carried on the Marian traditions in politics. So this was simply another faction opposed to the dominant one. But Caesar wasn't a revolutionary as he counted numerous bankers in his party and Syme points out that the Pompeians were more of a threat to the moneyed interests as they had threatened Sullan style proscriptions.