This is an excellent question. There was actually a war in 1962 due to border disputes and tensions are rising again. Even in Wall Street Journal article two years ago the author detailed what both sides are doing to show that they have control and what they will do to take control in the future. Hence, it is important for us to keep our eyes on what is happening between these two powerful nations. There are several reasons why these countries want control.
First, we should not rule out the issue of pride. No nation wants to lose face when it comes to land in view of a watching world (especially when there was a war). Moreover, to have more land is always a benefit for a nation. Who know what natural resources will be found in the future. Moreover, these lands can also act a buffer zone for further protection.
Second, part of the conflict revolves around Tibet. Tibet wants freedom from China and this is a problematic are in Chinese politics today. In fact, it is a very sensitive topic. India did not help the situation, when it sided with the Dalai Lama. In fact, India gave asylum to the Dalai Lama. There is still bitterness over this with the Chinese.