The key distinguisher is that China has a history of a few millennia of being the most powerful centralized state in the world, and India only has a few hundred years of sporadic unity under various foreign conquerors over the same period of time.and there was a time when the Japanese and the Koreans thought the same of China
Of course, if India were to get itself together it could be poised for a meteoric rise. Unfortunately, India doesn't seem to want to get itself together, and it doesn't have any real historical predecessor state to look to as an example for unification and achievement (except for those goofy maps of 'Bharat').
Imagine the Warring States are never unified, and Southern China fractures into some kind of strange feudal system, the Central Asians conquer bits and pieces of Northern China, and then the British show up and take it all over the course of a century. Then, this alternate China gains independence. This alternate China is roughly similar to what India is now. I wouldn't hold high hopes for this alternate China, and I don't hold high hopes for India.
Right now, India is full of bluster, with absolutely zero performance, historical or otherwise, to show that they are capable of achieving what they claim they will achieve "in the near future".