The economist notes that what Westerners take for granted--our economic dominance--is something that has been true only over the last couple centuries:
These two Asian giants, which until 1800 used to make up half the world economy, are not, like Japan and Germany, mere nation states. In terms of size and population, each is a continent—and for all the glittering growth rates, a poor one.
Until industrialization gave Western Europe an enormous productivity advantage that catapulted the West to dominance, the sheer size of India and China gave them the largest economies in the world. That was less relevant back then since there was little per capita surplus to make that economic size felt anywhere but within their regions, at best.
China, of course, is now the second largerst economy in the world as measured by GDP, having just passed Japan, a country a tenth the size in population. Which means that China is hardly as powerful as the GDP figure would indicate.
From the West's point of view, the relative decline of the West as India, China, and the rest of Asia have advanced economically, is really only a matter of European relative decline since American economic power has remained pretty stable as a share of the whole. We have reason to have confidence that our economic power has a foundation to keep growing even as China faces demographic limits to growth at recent rates and potentially worse outcomes.
And of the Asian powers rising, I'd surely call Japan a member of the West. And I'd add South Korea and Taiwan to that club with a little longer time to entrench democracy and rule of law after emerging from authoritarian governments in the last couple decades.
Further, India is poised to become a member of the West on the strength of its history of democracy and rule of law. So this is nothing to worry about when looking at India's rise.
Further, India and China are so large that they are perhaps better thought of as geographic terms (like "Europe" is today) rather than as political entities. Their very size and divisions could yet cause problems in rising further. Fragmentation is not out of the question, for either state. Although if I had to place bets, I'd give India a better shot at overcoming their divisions based on their experience with democracy and rule of law that provide alternatives to political separation as a means of satisfying grievances of sub-groups.
Just in terms of India versus China, their rise causes problems in that they will be nuclear powers who are rivals and neighbors. Yes, for conventional conflict the mountains between them will make them distant neighbors. But for nuclear weapons and diplomatic competition in Southeast Asia and Central Asia, the proximity will keep them focused on each other.
Yet India will have a geographic advantage over China that can overcome at least part of any Chinese advantage in head-to-head economic and power comparisons with China. China is surrounded by potential foes. These countries will lay claim to much of China's rising power. Indeed, China's rise causes a reaction by neighbors to counter China's greater power, nullifying at least part of China's increased raw power. India, by contrast, has few external foes that could divert them from focusing on China. Pakistan, certainly, diverts Indian military power and attention. And Burma. Toss in Sri Lanka if you'd like. But that's it.
Add in India's geographic advantage of being able to use sea power to block China's trade routes across the Indian Ocean and potential to use air power to interdict land routes to Central Asia, and India does not have to even surpass China in power to have the advantage in deployable power in a one-on-one comparison.
Add in America's deployable power, which will always be great because of our geography, and is far more important even with a rising Asia that has to watch neighbors carefully, and China has nothing to smile about in marking their rise to second place.
So yes, the question of whether India or China will win their economic battle is important, but it is not the only questions we have to answer when we consider the impact of their potential rise.