I believe that the rise to world power of Europe was essentially the rise of capitalism. And that Europe's disunity was indeed related to why and how the new economic and social and political forms associated with capitalism could arise there. It parallels the argument above about how scientific progress could continue in one nation when banned in another, but what is going forward is not abstract knowledge but the evolution of concrete industrial processes and the organization of the economy in general. These things are even more subject than abstract knowledge to censorship and interference by a powerful, centralized clique. There's just so much more at stake. If some philosophers argue about whether the Earth or Sun is the center of the universe, that might be troublesome. But if some jumped-up peasants are reorganizing the wool industry, that has immediate and widespread consequences that affect the revenues and political stability in the regions affected. A smart, pragmatic ruling bureaucracy might conceivably decide the progress involved is useful and beneficial and foster it instead of surpressing it, but by and large the powers that be won't be comfortable, the de facto bargains they've made with the underclasses will be broken, and it will be less trouble just to enforce the status quo.
But if there are lots of rival nations, there is a certain amount of chaos going on all the time in which innovations might insert themselves. A regime that is more canny or just lucky in fostering these reaps benefits in terms of increased opportunity for revenue, new technologies that might have a military application, and generally is favored over others that are in some combination more hidebound or less lucky. Competition has a selective effect that tends to shift the norms of politics to favor the rising bourgeois classes and their priorities.
I certainly would not want to write off East Asia as a possible earlier industrial giant. For one thing perhaps there are other approaches to rising technology than capitalism, though I'd bet they are slower. For another, conceivably Chinese society might "mutate" in a way that permits more competitive enterprise without regulating it out of steam nor sucking up all its profits in taxes. Capitalism in one empire might possibly take off after all. Finally, while China is typically unified there are a number of other smaller powers in the region, and conceivably some sort of capitalist constellation could arise among them--in Indonesia say. Then China might get drawn into this orbit despite all the factors that would tend to keep them aloof.
So I won't say it's unthinkable that a capitalist, or conceivably some sort of non-capitalist but still progressive industrial system, might arise in East Asia and be in the place the Europeans were in in say 1450, some centuries before that. If these East Asians can be where Europeans were in say 1750 around 1550, then the European expansion will find itself stagnated, with doors they were able to blast open OTL already held against them by powers as well able or better able to fight on the same higher-tech, higher productivity terms.
Under those conditions, with the prospects of the sorts of profits that fed the engines of capitalism in the early modern period curtailed, rival schools of thought might well tend to prevail; European competitive merchantilism might get regulated into stable order. Or Europeans might find themselves increasingly apprenticed to Asians, serving as middlemen in their empire-building.
Something I've seen in threads like this before that bears thinking about--the Europeans were motivated to voyage to the far ends of the Earth in search of wealth because they didn't have that much of it where they were. To be sure as productivity due to more modern methods of agriculture and goods rose, the standards of living rose (fitfully, for most working people, quite impressively for the better-off classes) and in terms of items of everyday use the Europeans were getting richer every decade. But Europe was not a source of many prestigious trade goods; when European traders made their way to Cathay at last, they didn't have much to offer in its markets. Eventually the Spanish for instance were able to tap some of China's key goods--by shipping silver from Mexico all the way to Manila in the Philippines, and then trading with Chinese traders there for the precious Chinese goods, which they then shipped on back to Mexico, and from there back to Europe. So only by the more or less forced labor of the Mexican mines were the Spanish able to manage this. The Dutch infamously conquered the Spice Islands and then massacred rivals to gain monopolies.
The question has been raised whether people who lived in the very homelands of these prized goods would choose to venture overseas in search of anything. Even if we suppose they might, they probably won't make targeting Europe a big priority. From their point of view the Europeans are sitting on the margins trying to deal themselves in or withdrawing in offended vanity.
Another factor is geography; certain European nations greatly multiplied their potential wealth by seizing control of vast stretches of the Americas. Would East Asians be so likely to manage to pre-empt control of the Americas from Europeans? They'd be coming in at the west coast rather than the East; they'd find the Rockies/Andes blocking easy expansion eastward, and most of the more highly developed Native American societies first. To be sure Eurasian diseases would be just as devastating to these peoples as they were to the ones that OTL were contacted and decimated east to west.
Still there might be a grace period for Europeans some centuries behind the Asians to nevertheless arrive in the Americas, and stake their claims--though in Mexico and Central America, they'd be quite likely to run into Asian-run situations directly. Still the Europeans would have their chances at part of what drove the great engine of capitalist expansion--loot from America.
But less literally so than OTL--if anyone is going to loot the Mexicans or Andeans, it would be the Asians first. It could be that without the lure of simple gold, the Europeans would not have turned to plantation economies in the Caribbean islands, and not discovered the profitability of crops like sugar cane or tobacco.
Or it could be the Europeans were just too slow and despite the inconvenient geography some Asian powers or other are already all over the central seas and from there, up the North American coast and down the South American one.
Without wealth extorted by forced labor from Native Americans and African slaves, it seems likely that domestic development in Europe would go slower.
It's not inconceivable that many Europeans would turn to service of Asian magnates who might have shown some passing interest in Europe, and in that service get taken far afield from Europe and get pretty well integrated into the Asian system. But these, while if emigrating in sufficient numbers would serve as a demographic safety valve, probably won't remit a lot of wealth to Europe nor return themselves.
Europe would be a neglected and poorer backwater, if capitalist or some other form of industrial progressivism continues to advance at all, it will be slowly and fitfully.
And that, I believe, will undercut the vaunted scientific tradition of Europe. I believe that the reason science advanced the way it did OTL in Europe had little to do with values, or traditions--it had to do with opportunities to employ new insights into how things work materially, for material gain. It may be that many scientists were not very practical people and they were in it personally for the thrill of discovery, but the institutions that arose to support them in this fun enterprise had evolved because societies that kept running into physical problems valued physical problem-solvers.
If some East Asian constellation of societies gets the wind of capitalist development in its sails, they too will refine scientific method, make world-changing discoveries and have transformative insights. And the Europeans, having much of the oxygen sucked out of their potential sociological blast furnace, will do a lot less of this.
A reduction in the opportunities for profitable trade overseas, combined with slower rates of industrial advance, rising populations hitting the limits of food supplies as raised by known methods but with not much to show in the way of improving those supplies--I'm afraid Europe would be a rather rough neighborhood to come from. Conceivably a major export would be hungry young toughs willing to serve as mercenaries; those guys won't come home either.
With the various kingdoms and other polities on the verge of unrest so persistently there would probably be a premium on authoritarian rule; this would tend over time to foster the unification of Europe into a relatively few dynastic empires, conceivably into one for the whole.
Europe would probably today be in a position like Turkey OTL--not quite as backward as some other places, with a lot of potential, but definitely not in the first ranks of the major nations.
