There is a problem with your question in that Buddhism and Hinduism both attempted and succeeded in spreading their religions. For starters, I would point you to this map showcasing Buddhist expansion.Buddhism originated in Northern India and yet ended up being practised as far as Japan and Indonesia. Ashoka the Great was the ruler of the Mauyran Empire that stretched across most of India, he was a Hindu in his early years but converted to Buddhism. In 185 B.C. he started a Massivemissionary campaign designed to spread Buddhism across not only India, but all of South East Asia and abroad. Ashoka banned animal sacrifices and discouraged people from eating meat, so in other words, Ashoka made sure that Buddhism would have a huge impact on the lives of people in his Empire; he even appointed Dhamma-Mahamatras to supervise people and teach them the ways of Buddha. Buddhism travelled along trade routes and that combined with large amounts of Zealous Buddhist missionaries, led to Buddhism penetrating into China and then into the rest of Asia.

Buddhism became so well known that it was written about by Roman historians like Plutarch. Buddhist missionaries were event sent as far as Greece, and it is recorded that Buddhist missionaries made it as far Macedonia, Epirus, Egypt, and Libya. The states of Southern India and states in Burma were also affected by Buddhist missionary zeal, and Buddhism soon spread there. With regards to Hinduism, while it never established the international presence that Buddhism did, it certainly did its fair share of proselytizing within India. Rulers would often give patronage to their specific strand of Hinduism and the various sects would each have their adherents who would try to spread their particular brand across the continent. That being said, Hinduism doesn't have a strong proselytizing culture, and for that reason Hinduism didn't really catch hold outside of India in the same way that Buddhism did. There are some small, dedicated Hindu communities in places outside of India, like in Cambodia, but they are very small.