I still believe it's worth thinking about, because running a system that taxes peasants in gold in an area where gold is not regularly produced requires a high level of organization. I'm not sure that thinking of "advanced" is particularly useful at any point, since it's usually asking the question "what society resembled us the most?", particularly given our present focus on technological progress. Comparing systems of resource extraction and governance is useful though for coming to an understanding of the constraints that states operate under and what sort of options are open to them in a crisis.
It's certainly worth thinking about, but not in the context of a thread on general technological advancement. For any sort of specific comparison, you need to look at the similarities and differences between two systems and figure out how they tended to react to a variety of circumstances. This kind of in depth comparison is ill suited for even an only general ranking of government systems, because what you tend to end up with are governments that are more "advanced" in certain areas, to various degrees of lopsided competence, hence the soldier analogy. By all accounts the Song administration was more "advanced" than that of the mongols, but that did it no favors when it was bloodily dismantled by Kublai Khan. As you say in the last quoted sentence, comparing administrative styles and systems is useful for understanding what options they had under pressure, but the variation in those options is precisely why they don't have much of a place in comparisons of linear technological progression.
Language barriers aside, this is what makes a comparison of Tang China and Byzantium so desirable, as they're both bureaucratic, tax-raising ("tributary", in the neo-Marxist way of speaking) states. A lot of systems have to function together, and comparing them is interesting. In Byzantium, land taxes had to be regularly assessed by imperial officials (the indiction), coin had to be minted and distributed in several types of metal, taxes had to be paid in consideration to any other sorts of demands the government may have placed on individuals (such as military requisitions, which would be counted against the tax paid). The whole system had to be enshrined in a legal framework to protect peasants from tax collectors and tax collectors from peasants. I have no idea about the details of how the Chinese tributary state functioned at the same time, but I'd sure like to find out.
The incredible similarities in most areas, contrasted with some significant differences in others, between middle Byzantine and medieval Chinese administration, court culture, and society in general have been a subject of interest to me for a while, but I think that a comparison of this is better suited to a separate thread. The Byzantine empire and China are a rare example of two very comparable administrative systems which arose in different contexts on opposite sides of the world, but what of the other myriad systems included under the umbrella of "medieval civilizations" which are not so comparable? Trying to establish a sort of ranking system for governments is like trying to establish a ranking system for philosophies. What would you end up with is a crowd of representatives from all corners of the field proclaiming the superiority of their system, or at least its superiority in one area or context.
Restricting comparison to two systems instead of literally every system is much more productive, because it allows you to establish the benefits, drawbacks, and differences between those systems without having to also compare them to those of every other system at the same time.
Technological advancements in the fields of mechanics, science, and architecture are much better suited to ranked comparison. Such advancements serve as an objective marker of progress, can be easily measured and compared in scale of implementation, and, in contrast to government types, they rarely have advantages and disadvantages, though sometimes two civilizations both have technologies that the other doesn't. These kinds of technological advancements can also be directly measured in the way they were implemented, instead of the potential response and mobilization by which governments have to be judged. Discussions revolving around this kind of comparison should be clearly quantified as such to avoid confusion, which this one wasn't, but I still believe it serves as the best way to measure the concept of abstract technological progress, though this admittedly generally didn't translate into anything of anything of much import for most of the middle ages.