It's more utilitarian authoritarianism versus fluid social democracy.
The Earthlings understand the value of a strong centralized leadership, that's been demonstrated repeatedly, they simply lack a rigid structure to enforce it and generally decisions are made through representatives with popular support. They're making decisions based on the welfare of their society.
While he's claiming a traditional form of authority (I.E. divine), using his sufficiently advanced technology and the superstitious natures of his subjects, Colonel Cugel's goal is clearly to create his own Spartan kingdom in the fashion of the civilization he worships. Even the religious-seeming rituals/displays are representative of that rigid ideology, in contrast to the children running about during Ledo's appraisal of the Gargantia - this cultist flavour is a rough parody of what Ledo had come expected from humans prior to his fall. It's very Heart of Darkness, after being very Moby Dick.
The conversation between Ledo and Chambers was fascinating. All too often, particularly in American SF, you get this big (DUN DUN DUNNNNNN) reveal and there's very little ambiguity to it. For instance, the movie classics Soylant Green or Logan's Run. They (the government, corporations, ambiguous authority) are undoubtedly considered wrong for their gross treatment of human life, or other obvious moral taboo breaking and that's it. Ignoring that maybe they could have a point. The hideauze and galactic alliance have legitimate differences - perhaps insurmountable - between those who value human civilization to near worshipful levels and those who remade themselves in order to exists completely without it. It's not surprising or difficult to accept that humans are fighting a war with other humans over differing beliefs. However, both here and in Soylant Green or Logan's Run it really comes down to the lack of agency the protagonist has in determining if those reasons are good or not - something they'd never have to deal with if not for accidental exposure to the Truth. If everyone knew that at age thirty they were going to be euthanized, and then were given the reasons why, the premise becomes more complex from a philosophical standpoint but less dramatic from a cinematic perspective. Ledo was lied to, his justifications, which required little in the way of critical thought or moral complexity, have crumbled. He can either re-frame his whole worldview, which is not easy even for a 15-16 year old, or rebuild that ideological comfort-zone that he's unknowingly been leaning on his whole life.
I like this show.