I do not know how much India have invested in education in the last 30 yrs, but during the early days of reform up to 2000s, China decide to invest in infrastructure rather than education.
The reason for the low investment is more money follows to infrastructure. Educational system has no use if the nation does not have infrastructure for educated people to work... Every years, much of India's educated elite immigrant to developed nations due to lack of opportunity. Education is indeed important, but lack of opportunity for educated will be a disaster. China see more of that problem in the recent yrs.
While you make a valid point it is also true that we are increasingly seeing a boomerang effect. An increasing number of the Indian and Chinese diaspora who sought higher education and work experience in Western developed nations are either returning to their countries of origin or making a significant impact by expanding business collaborations. However this impact cannot be maximized without a good infrastructure
The reason infrastructure is the most critical aspect of development is because it is a self propagating way of creating new opportunity. It is also the most important factor when it comes to urbanization- which is the first response to economic development.
Point being even if there aren't enough opportunities out there for the educated youth in China right now, with the solid infrastructure in place opportunities will keep increasing at a steady rate. This will also be a top down effect as in opportunities will present themselves outward toward smaller cities.
India on the other hand has already put a cap on it's growth because of a total lack of investment into infrastructure. The first and most visible effect of this is the disastrous process of unorganized urbanization. The second problem is that without adequate infrastructure, the gap between urban centers and rural areas has increased. The result is dysfunctional major cities, stagnant tier two cities and isolated rural areas.
Now this is not to say education isn't important, it is, especially for India who desperately needs to tap into the human dividend. So in many ways, you can consider education as part of the infrastructure. However without adequate physical infrastructure it is very difficult to impart education in rural areas, and here again we see a bottleneck for India's development.
Also dubious as it may be the Chinese government is extremely dedicated to education because it is their only chance to indoctrinate the youth, without appropriate indoctrination the consequences for the communist government in the future will be calamitous. But either way the physical infrastructure has made this objective easier.