Squealer got his power from being affiliated with Napoleon, and Snowball had equal power in the beginning until Napoleon ousted him.
From the beginning, Napoleon and Snowball are at odds. First of all, both were equally important pigs in the Jones days of the farm.
Pre-eminent among the pigs were two young boars named Snowball and Napoleon… (ch 1).
Squealer, on the other hand, is a naturally persuasive pig.
He was a brilliant talker, and when he was arguing some difficult point he had a way of skipping from side to side and whisking his tail which was somehow very persuasive. The others said of Squealer that he could turn black into white. (ch 1)
Napoleon and Squealer joined forces, and Napoleon wanted to be able to take over eventually. Snowball was in their way, because he was the other important pig. Snowball was “vivacious” but was not considered to have as much “depth of character” as Napoleon.
Snowball was a visionary and a believer. It was Snowball who had ideas to implement, who wanted to better the animals. He was “indefatigable” at organizing them into committees and helping them support the tenets of animalism.
Napoleon gradually developed more power, specifically because he was more interested in it than Snowball the true believer. He took the puppies and turned them into guard dogs. He used Squealer to convince the other animals of his side. He used Snowball as a scapegoat, driving him off and taking over. Squealer helped him explain away anything inconvenient.