It's true that China, because of its vastly larger population (more than 4x the size of the U.S. in 2011) will have a larger economy and military than the U.S. But if you ask people what they want in life they don't say ensuring that people with the same passport have lots of money and guns, they usually say happiness (and the assumption here is that money = happiness).
So the statistic everyone cares about is income per capita and PwC estimates the U.S. will have an income of about $85k per head while China will be poorer than the U.S. currently is with about $41k per person. (I'm taking their GDP estimates and dividing by population estimates.)
Gallup World Poll data also suggests that Chinese people will still be significantly less happy than the U.S. is today as Asian's tend to be far less happy than you would expect given their incomes. This may be due to weak religious institutions (religion and purpose lead to life satisfaction), long hours to acquire that income (people hate working), and in the future the negative impact of commuting (the worst part of people's days, and in crowded China commutes will be terrible).
Or was I wrong and most people care about having a big military and A-Rod's income?
Note: I'm not endorsing these estimates. I think they are an exercise in futility and my intuition strongly disagrees with the final numbers. India is projected to be vastly poorer than China, with about half the income per capita, implying China will grow just as fast as China over the next 50 years. I could see China continuing faster growth for a decade but eventually the transition to a modern economy will harmper China's growth while India's infrastructure (ports, roads, electrical grids) will enable it to increase its manufacturing sector. It's education and large English-speaking populace, along with its vastly superior political institutions, suggest it might be ahead of China by 2050. I'd bet on that.