From my perspective, the main factor contributes to the difference in FDI and economic growth in China and India are institutions. There are two kinds of institutions; one is formal institution, including political system, legal system and economic system, another one is informal institution, which consists of culture, business norms and ethics.
As for political system in India, which labeled as "sovereign, socialist, secular, democratic republic." It is similar to America, it has the federal form of government, its central government is patterned after the British parliamentary system, and several Parties are able to take control of the nation, but the main power to control the country is the central government. Compare with Chinese communist totalitarianism, India is more democratic in terms of the political system. In other, words, it is more easier to set up your own business in India and which may absorb more capital thanks to the democratic political system in India. According to the corruption perceptions index 2012, India got the score of 36, and China got the score of 39, the lower score means the country is highly corrupt in the public sector. Therefore, China is more attractive to foreign investors in terms of the corruption level. As for political risk, thanks to corruption and the departure of several key allies for India, the government has been weakened in India, which make India less attractive for foreign investment to compare with China. As for protecting intellectual property right, the provisions of intellectual property right in India is more comprehensive than Chinese, which ensures foreign companies get an easier access to take control of intellectual property in India. According to the data from Global EDGE, Chinese government provides more protections on labors to compare with India. Which is a good sign for encouraging FDI in China. According to Ease of Paying Taxes Index on Global EDGE website, which ranks the country