Although they are both strong leaders, Napoleon and Snowball have very different ideas about the revolution. While Snowball believes in the ideals of the revolution, Napoleon sees it as an opportunity to garner power for himself. Snowball has the brains, but Napoleon has the brawn.
After the revolution, Snowball tries to get the animals to work together, get educated, and be involved in government. Napoleon, on the other hand, wants the farm to be governed by an elite group of pigs rather than committees of animals.
Snowball is a strong orator, but Napoleon is a master manipulator. Ultimately, Napoleon’s power-grabbing is successful and he is able to not only run Snowball off the farm but continue to use him as a scapegoat after he leaves.
At the beginning of the novel, Napoleon and Snowball both feel a sense of superiority over the other animals. We see this through their assumption of leadership in the plans for the Rebellion. They work together to develop Animalism, for example, and teach themselves how to read and write so that they can run the farm once Mr Jones is overthrown.
After the Rebellion, however, the differences between Napoleon and Snowball become apparent. Snowball, for instance, tries to help the other animals and demonstrates a high level of patience. He sets up committees, like the Egg Production Committee and the Clean Tails League, and offers lessons in reading and writing.
In contrast, Napoleon's sense of superiority does not falter and this is combined with deception and arrogance. At the end of Chapter Two, for instance, he steals the milk so that it can be mixed into the pigs' food. In addition, he demonstrates "no interest" in the committees to educate the other animals.
Arguably, it is these differences which lead to the division between Snowball and Napoleon later in the novel.