This is a wonderful question, because it provides the opportunity to explore the meaning of the rise of China and India, and their various strengths and weaknesses.
But a key point I'd like to make is that the volume of engineers has no bearing on a country's competitiveness. Compare at the number of engineers in Redmond, Washington with the rest of the U.S. and the world; or compare the number of engineers in Schaumburg, Illinois (Motorola) with that of the rest of the world. In both of those locations, the number of engineers are very small, but they compete wonderfully.
Another key point: no matter how good those engineers are, quality of life in the west is almost guaranteed to go up. In fact, the west's quality of life will go up more if those Indian and Chinese engineers turn out (against the odds!) to be of overall fantastic quality. Look at the current reverse situation: the quality of life for the Chinese is enhanced dramatically by the smart engineers at Microsoft, Motorola, Nokia, Ikea, Starbucks (yes, Starbucks -- engineers have to design their coffee-making equipment and their furniture), Dell, Cisco. Similarly, the "West's" quality of life is enhanced by the good engineers at Samsung, Toyota, Mittal, etc.
Economics, fortunately, is overall not a zero-sum game.
That all said, the RELATIVE quality of life between India/China and the rich world has, and will change, dramatically. This is not necessarily a bad (or good) thing. For example, just 25 years ago, probably 99% of chinese led peasant lives with incomes of under $1/day. These days, the per capita income in Shanghai is greater than $5000/year, i.e., per capita income in China has gone up 15 times in 20 years in some places, while in the US it has probably not gone up more than 4 times. So while once the Chinese economy was probably 1/100th the size of the US economy, it is now about 1/6th the size of the US economy. At current mid-term growth rates, the Chinese economy (not per capita income) will exceed the size of the US economy in about 40-50 years.
The overall competitiveness of an economy is probably little related to the number of engineers. Certainly important factors include: general education, capital allocation efficiency, government and regulatory efficiency, freedom of movement, political stability, health care, level of anti-social behavior. In many, but not all, of these areas, the U.S. is far superior than China or India.
95%+ of Chinese can read and write, only 40% of Indians, while 20% of U.S. students do not graduate high school. Political stability is very strong in the US, less so in India, and less so in China. (Some may disagree with this assessment of China, but I would only ask, "what happens if Hu Jintao has a heart attack and dies"? The answer: "no one knows."....THAT is political instability.)
US banks are the best in the world, while Indian and Chinese banks are terrible. Default ratios in the US are under 1%, in China closer to 30%, notwithstanding the high debt in the US vs. the growing economy in China. If China has a default ratio of 20-30% now, imagine what happens if the economy slows down!
China and India are also terrible at allocating labor efficiently. The US is fantastic. Just about anyone in the US can go just about anywhere for a job or to start over. Most Indians and Chinese are stuck in their peasant villages or depressing cities.
The level of efficiency of the US government and the local and state governments are excellent compared to their Chinese and Indian counterparts. India has 30 million cases in its court system, many lasting a decade or longer. In China, local governments threaten audits if a company wants to move, while major league corruption is endemic in both China and India.
So long as the US maintains labor flexibility, efficiently allocates capital, promotes education, maintains a good set of political checks and balances (thereby promoting stability), the Western engineer and his non-engineering friends has no need to worry about large numbers of poorly trained, poorly informed, poorly managed, poorly allocated engineers.