Surly: "I doubt that anyone knows."
No, of course no one knows.
the US is still the undisputed master of advance weaponry and it's nuclear arsenal is intimidating.
True. But those nukes are a doomsday option, nothing more; i.e. they are not a real option.
My mind instinctively tells me that those two populations cannot be sustained without walking into a brick wall of total resource depletion from everything to food, water, clean air, health, energy etc.
We could discuss each one of those things. I have discussed them to some extent throughout adjacent threads, and in the old china potpourri thread going back a few years. Most of my posts presenting real options and solutions, and effective or semi-effective initiatives underway, are ignored, or are waved-away with vague generalities and statements of religious faith. Which is OK, since I enjoyed writing the posts anyway. But just to let you know. You can verify what I say if you want to dig far enough back.
Bottom line: humanity is capable of addressing all those things. The earth is finite, but human ingenuity and industry are not. Our present civilization could be said in the year 1850 to be outright IMPOSSIBLE. At that time, we were limited to wood and coal and whale oil, and given those technologies, our current civilization really was impossible. But now it is possible. In the year 1980, the idea of using solar panels to power heavy industry seemed outright IMPOSSIBLE. Far too expensive, raw materials, fabrication costs, blah blah blah. And that assessment was true: it WAS impossible, given technologic development at that time. But now it is possible. And lots more things are becoming possible, every year. Material resources are finite, but our ability to use them in progressively smarter ways is not. There is no "brick wall".
Another way to say all this is: things change. Wonder of wonders, things change.
Humans can address all those problems. Whether they WILL or not, remains to be seen. Maybe we'll blow everything up before the problems get solved. I don't know.
I also have a problem in this area of ashamedly having to admit I am still a peak oil adherent, even in the face of the current situation we are in. Having been convinced of this by folks like Nicole Foss, Kunstler, and of course a great many others; I think they were just early.
Early, and now blindsided by shale gas, which is just now starting to get geared-up in Eurasia and elsewhere. As I've said repeatedly, there's a crap-load of nat gas in Eurasia, easily enough to last a century even at much accelerated rates of use. There might be some oil-crunchy things coming down the pike over the next couple decades, but nothing at all like the peak oil doomers were saying 10 years ago. There's too much of the stuff.
Another problem ("problem") is that the crashing cost of renewables is about to open up new vistas of FF retrieval. There has been concerned discussion of this on realclimate.org's forum (some very smart people, a lot smarter than me) and elsewhere. Cheap, super-high-EROI renewable power makes it possible to retrieve FFs that would otherwise be stranded because of low EROI. And of course those FFs will be burned, releasing CO2. The future is, hence, NOT all rosy with cheap, high-EROI renewables. We have to somehow keep the damned FFs in the ground where they belong.
My second problem is the rich poor problem that has developed in China. The poor in China, hundreds of millions alone I read that are camping out around major cities waiting for jobs an witnessing how the lucky live is a ticking time bomb the way I see it. They are not on a food stamp program like the US, getting a welfare check every month, or living in section 8 housing.
The difference is that money goes a lot farther in China than here. An annual income of $12,000 IS middle-class in China, because most things are relatively cheap. You are right that there are class-related pressures building in China. But I think maybe less than you imagine. Per capita GDP in China is a little under $8K I believe. They have a poverty rate a bit over 12%; people living on $1.25/day or less. That's a lot of people. Though consider in relation to 40 years ago: 90% poverty rate! Consider also that the large majority of people who are NOT impoverished have a stake in seeing the system continuing roughly as it is. The system is growing and giving everyone a somewhat better standard of living every year, so why not continue it?
If the current situation can continue and be sustained somewhat like it is and these resource and rich poor problems can be solved, as Alan believes, then yes, China becomes the Boss Man.

Just to back up for a moment and take a MACRO view: it really is not "China" that becomes a boss man. It is intelligence, sound leadership, good planning, boldness, efficiency in execution, wisdom in resource use, and suchlike that becomes boss man. If China has more of that stuff than others, then...