None of the historical Chinese dynasties outside of maybe the Qin had great standing armies and the blame for that has to do with the life style of native Chinese vs. "barbarians." The best weapons in the world can't make up for the fact that "barbarians" were raised from birth in violent, chaotic environments where it was kill or be killed. Nurhaci was 23 when he became chieftain of his tribe, 25 when he launched his first war, and 34 when he crushed his other Jurchen enemies and became de facto ruler.
By contrast, the average Chinese would be most unfortunate to see battle even once during his entire life, and maintaining a large standing army was next to impossible so the vast majority of soldiers were drafted farm boys with a few months of basic training. Combined with the lack of horses and riding skills - again due to life style - it's no surprise that Chinese armies punched below their weight the vast majority of times vs. the "barbarians" even with superior equipment; and even less of a surprise that the Warring States armies fared relatively better than later Chinese dynasties, since during the Warring States, far more Chinese actually grew up fighting than farming.
Any way, we don't live in the age of farmers vs. "barbarians" any more. Industrialized armies all tend to be drawn from the same sort of population - sedentary civilians - so it actually is about technology, economy, and organizational competence these days.
Well, although the settled farming society has its inherite disadvantages like you said, I can't say that life style of settled farming is much of a draw back when properly addressed. For example, Han and Tang had many state owned horse breeding ground near the frontier regions. Whoever raised the horses were certainly good at riding them just like the nomads. Most Chinese dynasties also had the system of hereditary military system such as 府兵 in Tang, 军屯 in Han, the banner men in Qing. These population spent much more time in military excersize besides farming, they don't pay tax or crops except anything enough to feed themselves, pretty much like the nomads spending time in hurding their livestocks.
The result is that many dynasties did very well against "barbarians". Han and Tang's standing armies weren't big but very competent, they annialated the states of Xiongnu and Turks, especially Xionnu disapeared as an entity all together. If you read the record of those expedition of Han and Tang, you will find that their numbers were only higher than their oponents because they had people to transport food, while the nomads'food (live stocks) had legs. One can't really use that number difference to judge the fighting strength.
What made Song standing out is 1 they lost the horse breeding ground, therefor lost mobility and speed, 2 very bad administration and deep mistrust of military due to the fact that the dynasty was founded by military coup. The 2nd point is the decisive factor as the soldiers were poorly treated (just better than criminal), the generals feared their own emperors than the enemis. The 1st point was much less of an issue compared to the 2nd as Ming dynasty's funding showed. Ming dynasty started from the south just like Song without many horses and yet overthrown Yuan who still held most of the cavalry forces. Ming was even able to sack Karakorum, the capital of Northern Yuan.
The conclusion is that although number and quality of arms, life-style do play important roles, nothing is as decisive as orgnizational efficiency and determination.
