If we're talking about the Indo-Aryan tribes that settled in India during the 2nd millennium BC, then having them migrate to China instead would have a huge impact on world history. With Indic cultures gone from India, the entire ethnic, religious, cultural, and historic makeup of the Indian subcontinent would be radically different. Hinduism as we know it would not exist, for instance, but instead would be an amalgamation of indigenous Dravidian and Austro-Asiatic cultural elements, somewhat more, I imagine, like the animist traditions of pre-Hindu/Buddhist Southeast Asia. Without Hinduism, there is also no Jainism, Buddhism, or Sikhism; there is also no spread of Hinduism and Indic courtly culture to Southeast Asia and Indonesia, so the history of that region would be quite different as well. No Buddhism means Confucianism and Taoism remain the dominant forms of spirituality in China, and the religious makeup of Korea and Japan would also lack OTL's Buddhist element. In fact, if the Indo-Aryan tribes settle in China instead, China's whole history is affected to such an extent that Confucianism and Taoism may not even exist; likewise, the dynastic history of China would be completely different.
No classical Vedic Hindu culture in India would likely also affect the history and development of Iran and West Asia - assuming the Iranian tribes, having split from the China-bound Indic tribes, still occupy the same lands in the same time frame as in OTL. Early dynastic Iran may be affected in some way by a non-Indic India, as might be any Hellenistic empire that later arises. The effects, in fact, continue long past antiquity. No Buddhism would affect the later development of historically Buddhist peoples such as the Mongols and Tibetans, and given the sheer mass of butterfly effects that would build up over the centuries, virtually nothing we known from OTL Eurasian history would still be identifiable in this ATL. A fascinating idea, Nihao!
