How did Han Fei Tzu's beliefs differed from the beliefs of Confucius?

Confucius thought all men were basically good, Confucianism believed that family came first, children should honor their parents. If the family was happy, the people would be happy and consequently, the king would find it easy to rule with a gentle hand. Confucianism also believed in a hierarchical society, that everyone had a place and a job. There is very few opportunity to deviate from that order. If you family was a farmer, his son also was a farmer, a soldier's son also a soldier, a statesman's son becames statesman.

Han Fei Tzi was a Legalist. In Legalism people were thought to be bad in nature. They needed laws and regulations with stiff punishments to keep them in line. It was a harsh system, very Macachiavellian in nature. It promoted the better skilled person over less skilled people. It's a dog eat dog society, if you don't eat you'll be eaten. Upward mobility was possible but at a cost of loosing the polite and courteous society which Confucianism provided.

In the end, China used Confucianism to pacify the people but kept the legalistic regulations which govern the country.