Mao Zedong and the Communist Party of China were victorious over Chaing Kai-shek and the Kuomintang for a number of reasons. The most important reason, however, was the ability of Mao to mobilize the lower classes of China. Because most of China was populated by peasants, this meant that the communists had a sizeable numbers advantage in the Civil War. Chiang Kai-Shek's cause was wracked by scandal and corruption and most Chinese viewed the nationalists as exploitative.
It can be said that Mao Zedong was a stronger leader than Kai-Shek but at the same time, the Nationalist forces were decimated by years of warfare with Japan. While both sides fought Japanese occupation, Mao conducted a hit and run type campaign with minimal casualties. The Nationalist side was more involved in direct confrontation and suffered a much larger casualty rate. Also, Zedong's forces were blessed with a cache of weapons left behind when the Japanese evacuated.
Both sides of the war were supported by other countries. Mao Zedong was funded by the Soviet Union while Chiang Kai-shek was funded by the United States. Despite large investments on both sides, Mao's side utilized the resources more efficiently and the Soviet Union's aid was better coordinated. It seemed like a lot of American aid was used in an inefficient and corrupt manner.