There is exactly one objective criteria that societies can be judged by in any frame of reference, ancient or modern. That is survival. After all you have to be in the game to play it.
This isn't to say that other criteria aren't important as well but ultimately these are subjective and limited in their ability to compare across broad sweeps of human history. It's not really fair to talk about Qin dynasty China in terms of its ability to secure the rights of life, liberty, and the pursuit of happiness or the consent of the governed. They weren't even thinking of politics in terms of the individual in this era (though it's not 100% clear to me that the writers of the declaration were thinking entirely in individual terms either, too many signs of corporatism). Their reality was simply too much different to be judged in our terms.
Of course, judging societies by their ability to survive should mean more than just counting how many years they were around. I see three basic qualities, the ability to project power, the ability to maintain stability, and the ability to spur internal development. How these three are framed and recommendations to enhance these qualities very highly across eras, though modern conception certainly seem more effective then older ones.
The reason I regard survival as essential is that other conceptions have what I see as a fatal flaw. That flaw is that while looking at a society at any given time may make economic development, human happiness, or simply responding to people's preferences seem important, in the longer term if society makes the wrong choices reality will come along and mug it, no matter how happy the people are or how well it responds to people's desires. Reality is a harsh mistress, the wrong choices will leave society broken and in pieces, even if every step along the way conformed with the current thinking on how a society should work. The success of a society can be judged by its ability to recognize, and effectively confront, those problems that threaten its long term survival. A society unable to do this is ultimately a failure. While at the time it may be obvious, to history there are right and wrong choices and we will be judged against those, not against how satisfied we are with choices in the moment.
Of course, less than effective societies can survive for a rather long period of time by a conjunction of social forces, such as location and being non-threatening. Since this survival is not due to a society's conscious choices but the choices of others it is more of an exception that proves the rule than something to take guidance by. In any case, this isn't an option for a state of the US's size and ambition so isn't really an option for us. We've already developed enough of a reputation that even if we set aside our ambition I highly doubt we'd be left alone.