While Snowball and Napoleon created the basics of Animalism as a team, along with Squealer, as their power increases, so do their disagreements on how Animal Farm should be run.
The two cannot agree on plans for Spring, or how best to defend the farm from attack. However, the biggest issue arises due to Snowball's desire to build a windmilll. He feels that it will increase production and make life easier for the animals. Napoleon is opposed to the idea because he wants the animals working to increase food production rather than wasting time building a windmill.
Snowball is very good with words, Orwell describes him as a
[...] more vivacious pig than Napoleon, quicker in speech and more inventive
Because of these traits, Snowball is able to garner support for his windmill project. However, just before the animals are about to vote in favor of the windmill, Napoleon releases a weapon he has been hiding. The nine pups that Napoleon had taken from their mothers were raised to be his bodyguards and they chase Snowball off the farm.