Like Stalin, Napoleon becomes dictatorial, demanding that people serve him well. He creates propaganda, tainting the truth to suit his aims, just as Stalin did. When others doubt him, and they challenge some of the issues, Napoleon has the vicious dogs attack the offender. Others are forced to confess to actions they have not committed and are done away with, just as Stalin had millions of his own people killed. Anyone who lived feared and dreaded him because of his police terror, just as the animals live in fear and dread of Napoleon and his wild dogs.
Like Stalin, Napoleon had several allegedly disloyal animals, including many who had been important in the revolution, executed. Several of the hens, who did not want to give up their eggs, revolted and were executed, as were several pigs who confessed to being sympathetic to Snowball. The first evoked memories of peasants who were executed because they did not want to give up their crops to meet quotas, and the second may remind readers of officers and loyal communists who perished in some of Stalin's purges.
One major similarity is in the way that they both created cults of personality around themselves. Napoleon did this by using Minimus to make up things like the hymn to how great Napoleon was. Stalin did the same thing by setting himself up as the father of his country and the source of all good things.