This is a story I read in the local paper in Delhi which is actually originally published on CNN about an American girl's experience of her trip to India:
http://edition.cnn.com/2013/08/20/wo...rpt/index.html
In India you have strong religion and weak government.
In China you have strong government and weak religion.
You have to remember that life is cheap in India..... sexual harassment, rapes etc are committed by rural/tribal people who have ZERO education and ZERO money (GDP per capita is less than half of China). Their life is not worth a whole lot. Sadly in India, most of this kind of thing is targeted towards one particular section of society - the orientals, who make up about 10% of the population.
Other crimes are pretty low..... this is the main crime. This is a country which basically has (practically speaking) no government, its run by the wealthy class. But its important to note that women are not treated this way in India - this behavior is limited to a very small section of the poor/uneducated class which is in fact more than 80% of the population (of 1.3 billion).