Snowball and Napoleon have contradictory ideas. Snowball wants pure communism, where everyone benefits equally. Napoleon, on the other hand, prefers power. These characters represent the struggle between the ideal of communism and the implementation.
Under Jones, both Snowball and Napoleon were “pre-eminent among the pigs” (ch 1). When the animals first take over the farm, Napoleon and Snowball work together. It becomes clear very quickly that Napoleon is less of a talker and prefers to be behind the scenes and in control.
Snowball was a more vivacious pig than Napoleon, quicker in speech and more inventive, but was not considered to have the same depth of character. (ch 1)
It does not take long for Animal Farm to be a contest between Snowball’s brain and Napoleon’s brawn. Snowball has the ideas. He arranges the animals into committees while Napoleon is secretly consolidating power. Snowball also comes up with the idea of building a windmill, and Napoleon disagrees until he realizes it is a good way to keep the animals distracted.
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This is a good question. The conflict between the two pigs grows in the beginning of the book.
Snowball is the more intelligent pig. He has foresight and is forward thinking. He is able to see the big picture and plan for it. This is why he wanted to build a windmill. He realizes that if the animal's lives will be easier, then they will need technology. He even gives a discourse on the power of electricity. Needless to say, Snowball is the better speaker. He is also an able fighter and was awarded for his bravery.
Napoleon, on the other hand, was underhanded. He was plotting all along. In particular, he saw the importance of power, even if it was brute power. So, when the opportune time came, he drove away Snowball with the aid of the dogs. Then he claimed the plan for the windmill as his own. He was also more practical. He thought they should run the farm to get food.
The conflict, then, is one of the ideology of communism and brute power. Another way to look at it is as a conflict between forward thinking and immediate action.