This is a good question, as Snowball is clearly the better speaker, intellectual, and planner. Therefore, it is interesting that Napoleon won out in the end. He did three things in this chapter to garner power.
First, Napoleon is able to get the animal on his side. In other words, he is the better politician. Moreover, because Snowball is thinking of many ideas, such s the windmill, Napoleon has the time to spend time with the animals.
Second, Napoleon has trained the dogs, which he took earlier to be his muscle. With these dogs he now has brute strength. In the end, strength makes right. We will see this in action later on in the book.
Third, Snowball may be the better speaker, but Napoleon has Squealer. Squealer is a great propagandist. With Squealer's help, Napoleon is able to justify whatever he want to do with rhetoric, which the other animals buy.