They are probably the most unified, homogeneous nation state/culture ethnicity on earth. China is probably far more stable than the baby US.
history can't support your image of china or chinese.
Then show me some history.
China is by far and away the most unified and self identified ethnicity/nationality on earth. Like 30 times moreso than the US.
if this is at the core of your presumed chinese stability, i would suggest revision.
rather than homogeneity, there's over 50 different chinese ethnicities and a dozen regions which separate the country with greater diversity than those which separate the US. for example, there are also a dozen languages spoken by chinese which aren't intelligible with mandarin, which maybe 2/3 of the country speaks. within each of these languages are dialects which further isolate individuals to the locations which red china insisted they remain for 30+ years. i think they all write the same, relatively.
here's some history (...from the top of my head, so figure a +/-):
the taiping rebellion corresponded with our civil war, but lasted considerably longer and smoked some 20,000,000 chinese. it was an assualt on a western-corrupted government by a force of poor chinese...failed
1911(?) the qing dynasty, the corrupt government from above, finally falls to another generation of broke chinese exploited for their labor... enter the republic of china and start the struggle to maintain mongolia, taiwan and tibet under chinese control.
the country was not stable until the commies took over... there were warlords - ethnically and regionally devisive forces running amuck, while we were pulling together through the great depression and building our new deal infrastructure. war after war in the 20s were fought to consolidate the country, then the chinese colluded with and were double-crossed by nazis, finding themselves at war with japan.. again
coincidental with WWII, mao rustled up the poor masses of chinese in the west and pressed the republicans out of the country in some 6 years... they fled to taiwan. that rule has struggled to control tibet and some other issues, but have been effective in controlling, isolating and impoverishing the chinese...again. since mao has died, and commensurate with exposure to western influence and the affluence of the coastal cities, china has dealt with unrest related to their labor practices and government corruption - the very mechanisms on which their industrial complex is run.
a lot will depend on this perception:
what's not out of left field is that china is overdue a recession which has the potential to be exacerbated by stagflationary forces to include coping with that massive population you point out.
Odds seem far better that the US will hit that wall.
China's growth is based on actual fundamentals whereas 70% of our economy is in the service sector, which means it can evaporate on a whim or a wind. Our biggest industry growth sector is healthcare! Think about it! And virtually every other sector of our economy is stalled or in the midst of radical decline.
We don't even have a plan or a hope for recovery.
Even Gates says his greatest fear is that we will have to gut the military to address our budget. Duh! We will have to gut everything to address the budget.
We are way beyond broke.
the one thing that china's growth predicts is that it can't be sustained at the current rate, your observation of the intrinsic value of the yuan alone indicates a long-winded effort by china to buoy the chinese economy by postponing deflationary implications of its growth, a circumstance less sustainable than this concept of the US being broke. while you've argued that china stands a chance of operating independent of developed economies, i contend that that is impossible. chinese economic activity is decidedly external at this juncture, and they have a long, long way to go before they can be seen as a consumption-based economy capable of supporting their own output. our trade deficit, for example, indicates a country which consumes. our manufacture, despite being the largest in the world, is eclipsed by our consumption - dramatically inverse to china.
should the current issues affecting deflation in the chinese housing market, the current decrease in overseas demand, the current layoffs and public/private finance issues... the hundreds of billions of loan defaults currently derived in their industrial complex... should all of that amount to an economic downturn trailing western markets' trends by signature, china will have to confront their populace. will the behavior of just 80 years ago rear up again? will they deal with the same labor upheaval that the US did when we came storming on to the industrial scene a century ago, or like history shows, will the chinese version be worse, longer and bloodier? when they emerge, will they return to their roots like the US did? if so, where the US became a bastion of trade and world influence, china will become a sleeping giant for another century to wake from hibernation.
stability, homogeneity and nationalism cant be associated with china, particularly with some exposure to foreign wealth. persistent growth cant be associated with economics, especially with as many patched up factors as china's playing with.
i think china will lull a bit, and be challenged this decade, far from taking any sort of lead.