Buddhism was around 500 BC. Hinduism prevailed well before that, many a thousand years, so India was much ahead in Spirituality, texts, books, enlightened people etc. India was way advanced in all aspects. vedas (rituals), Ayurveda (medicine), Yoga (path to moksha) sutras, Upanishads, Gita etc etc..

In China, the only reference to any spiritual texts were of the "Old Saints" on Taoism and confucius were about the same time as Buddhism, about 500 BC. Taoism, was based on a Chinese text summarized by lao Tzu a Chinese historian/ Librarian.

Buddhism as a religion, is said to have been passed by "Transmission beyond Scriptures" from Buddha, all the way down in a hierarchy. The first was Mahakashyapa. the 28th was a prince, from South India the third son of Pallavas called Bodhidharma. he became a buddhist monk , went East, went into China and started preaching Buddhism. Buddhism, the main "Vehicle" called the Mahayana sect, which believed in meditation as their path, was the one that was made predominant in China by Bodhidharma.

The sanskrit word, "Dhyana" became "Chan" chinese for meditation in China. later, it moved further into many neighbouring countries like Tibet, Srilanka, Burma, Thailand etc and finally reached Japan.

It is believed that the conservative culture of India, with so much introversion, provided the seed for Buddhism. A seed is very reserved and inward looking, ugly, but packed with all the goods. China provided the fertile land and opening for the seed to really sprout and grow into a big tree. It later, really blossomed into a ritual, beauty, practice with the poetic/painting forms as Zen, meaning meditation (Zhazen) in Japan. So Buddhism became a part of culture, where everything is done with "awareness" and beauty including making a cup of tea and drinking it.. bowing saluting is also such a tradition and done with full awareness.

Buddha, was pretty concerned by the reaches of vedic traditions and rituals had become too dominating for the religion with priests and the elite pushing things to the limits. When Buddha, after realization really questioned the existence of Athman and Brahman are really went opposite to Hinduism.

While we believe in a soul, athman and its union yoga, with the paramathma. supreme which is all powerful, Buddha decided not to speak of the powerful of the supreme and not preach the existence of  athman.. but called that there is really a void in the center and aptly called it ANATTA, in pali which is opposite of ATTA, atman..

Rather than calling the individual ego/identity soul's culmination with supreme as moksha, he used the word Nirvana, which actually means Blowing out like a candle's flame.

Hinduism, looks at individual as a drop that seeks merger with the ocean.. Buddhism says the drop is insignificant, lost part of the ocean and when it merges it ceases to exist.

To-may-to, Ta-mah-to  it is all same  but Buddhism is easier to grasp for the new age rational mind.