Confucianism has a core of morality, ethics, and activism. It encourages social harmony and mutual respect. Confucianists sought to perfect their character by living a virtuous life and seeking goodness. They valued ethics, respect for elders, and propriety. Confucius, the originator of Confucian thought, believed political order would be found by the proper ordering of human relationships, and so did not bother himself with the structure of the state. He stressed that a good government must fill their positions with well-educated and conscientious people, called Junzi. Confucius was followed by his disciples Mencius and Xunzi. They also possessed the same optimism that humans could improve themselves to perfection.
Daoism has a core of self-reflection and oneness with the cosmos. They refused to meddle with problems that they thought defied solution, and were the prominent critics of Confucian activism. They devoted their energy to introspection, in hopes that they could better understand the natural principles of the world. The central concept of Daoism is Dao, roughly meaning "the way of nature". The exact definition of Dao is unclear; it is portrayed as an unchanging, passive force that "does" without "doing". Daoists try to follow Dao through Wuwei - complete disengagement from competition and activism, and instead living in harmony with nature. This philosophy discouraged the presence of any government or empires, just small self-sufficient communities.
There are a few similarities between Confucianism and Daoism. They were both created as a solution for the chaos that emerged from the fall of the Zhou Dynasty, although it was the arrival of Legalism that created unification in China. They both focus on self-improvement: Confucianism in the form of relations with others, and Daoism in the form of relations with oneself and nature. Confucianism and Daoism clearly have strong contrasts, but many people believe that for a person to be whole, they should incorporate elements from each.
Sources:Bentley, Jerry, and Herb Ziegler. Traditions & Encounters: A Global Perspective on the Past. 181-89. 3rd. McGrawHill, 2004.