What caused the shift from hinduism to buddhism?

You did not specify which country this religious shift took place however, India is the country that is dominant with Hinduism. The shift took place in 300 BC where Buddhism became very popular because Emperor Ashoka was facilitating its expansion. But up to present, Hinduism still remains as the dominant religion of India. In other parts of the world like Tibet and China, Buddhism is the dominant religion.

From the man to stop suffering which made more budda which began the rein of buddhism