Why is it that most graduate school aspirants in India prefer to apply to the US instead of comparable universities in continental Europe?

There are several reasons which I can think of. First of all, it is the mentality of the Indians in general. They see most of their seniors and peers applying to US universities, so they also decide to go for it. The information about the different universities, their course structures, application procedure for the US universities is readily accessible to them. The marketing of the US universities is much better than the European ones. A major share of the latest ground-breaking discoveries and innovations seem to be from the US. Since the overall number of universities in the US is much greater than in any given country in the EU, the students have more number of options to choose from. Even if some of the courses in European Universities might be in English, still they have to live in a country whose primary language is unknown to the Indians in most of the cases. They anticipate this might be troublesome in their day to day experiences. PhD programs in the US follow a structured path, at least initially, where you have all the rules and regulations in place for taking course works, choosing an adviser and so on. It makes the whole process very systematic. The PhD programs in the European countries is not so well defined in the sense that in order to get an acceptance, first you need to find a professor who will be willing to supervise you. The professors have greater say in the admission procedure in European countries. Generally, the completion time for a PhD in the European universities is about 3 to 4 years while it could be anything from 5 to 7 years in a top ranked US university. The primary goal for obtaining a PhD from Europe is getting knowledge in the state of the art technologies and learning how to do research. On the other hand in the US, you need to have some original contribution to your field before getting your PhD. For these reasons, PhD from an US university is sometimes valued more than that from their European counterparts. So, doing a post-doc after a PhD from Europe is very common, but if you can do brilliant work during your PhD in the US, you have a chance of getting a faculty position right after your PhD. Also, US has got a large number of Indians when compared to other European countries. So, the Indian community in and around any US universities is pretty large and  the students don't feel so much out of place. Indians are more conversant about the job market in US after completing graduate studies while in most of the cases, they do not have a clear idea about the job scenario in Europe. Indians have a better exposure to the US culture, thanks to Hollywood and numerous American T.V. shows. Naturally, America is the place where most people want to be in.

Anurup Dutta gives very good answers. I would like to add to that (having gone thru the question process myself). Here goes: a) The choice for preferring the US over Europe has largely to do with the perception that life in general for the aspiring Indian grad student is going to be comparatively a lot more difficult. Whether you accept this or not - I am just sharing what typically goes thru the mind of that student. b) Life after grad studies is also a huge factor. It is generally the same perception that getting gainful employment - whether research or practical application of one's newly acquired skills - can have an impact on their own life and of course the community surrounding them. c) Language barriers (remember I stated earlier "perceived"), still lurk somewhere in the decision making process. Even if the grad work is conducted in English, administrative headaches, and other bureaucratic issues only serve to inhibit this. Well in the past for example many places in EU wanted certified translations, authentications, evaluations (or establishing equivalency), etc., before even considering inclusion or admission. Such steps only dissuade folks from placing it on their top50 lists :-( d) The funding avenues you mention are a small fraction of what is usually on offer from North America. Extremely limited and one has to go thru many hoops just to get anywhere close. Hope that helps answer it bit...