Which two animals on the farm disagree over every decision in Animal Farm?

Napoleon and Snowball always disagree.

Old Major is the prophet of Animal Farm.  Before his death, he laid out the goals for the new life that the animals would have.  This involved the animals being self-sufficient and living the good life.  The animals would share ownership of everything, and no one would own anyone else.

After the animals take control of the farm, the pigs rise to domination quickly because they are smarter and considered leaders.  There are two leaders vying for control of the farm: Snowball and Napoleon.  Snowball is a true believer, and Napoleon just wants power.

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. 2)

Napoleon’s plans are secret and long-term, but Snowball believes in collaboration and idealism.  For example, Napoleon takes the puppies and secretly trains them to be his guard dogs, and Snowball spends his time making elaborate plans for a windmill that all of the animals can enjoy.

Eventually, Snowball and Napoleon cannot coexist. 

These two disagreed at every point where disagreement was possible. If one of them suggested sowing a bigger acreage with barley, the other was certain to demand a bigger acreage of oats …. Each had his own following, and there were some violent debates. (Ch. 5)

When the farm is established enough, Napoleon pushes Snowball out and takes full control.  Snowball becomes a scapegoat for everything wrong that happens on the farm.  Napoleon has full control, and Snowball is nothing more than a tarnished memory.

Napoleon and Snowball represent two different approaches to communist leadership.  Snowball believed in communism for the benefit of the people, and Napoleon believed in using communist beliefs to subject his people to his will.  In the end, Snowball was too idealistic and Napoleon too cunning.