In William Golding's Lord of the Flies, the conch is symbolic of the order of society while the pig's head is symbolic of Beelezebub and the chaos of demonic power. Thus, they are representative of two different aspects of man's nature.
In the first part of Golding's allegory, the conch is respected and responded to by the boys. They come in an orderly way to their meetings, they do not speak unless they hold the conch; they act civilized. But, by Chapter 5, anarchy begins when Jack ignores the conch and shouts over Ralph's insistence on that the rules are all they have:
"Who cares?....Bollocks to the rules! We're strong--we hunt!"
It is at this point that Simon becomes "inarticulate in his effort to express mankind's essential illness." And, Jack and the hunters steal the fire and leave the head for the beast. Simon, who has hidden himself in the leaves, looks at the head after the others depart:
The half-shut eyes were dim with the infinite cynicism of adult life. They assured Simon that everything was a bad business....the Lord ofthe Flies hung on his stick and grinned...and his gaze was held by that ancient, inescapable recognition.
Intuitively, Simon recognizes the pig's head, "Lord of the Flies"/Beelezebub as the evil that is inherent in man. Simon tries to insist that he is merely "a pig's head on a stick," but the Beast retorts,
"You knew, didn't you? I'm part of you? Close, close, close! I'm the reason why it's no go? Why things are what they are?"
It is, of course, after this incident and the theft of the fire that anarchy rules on the island, replacing the civilization of the rules and the conch.
Interesting question. In Lord of the Flies the power of the conch is clear virtually from the first moment it's found--it has the power to unite the boys. Soon it becomes the sign of order and discipline, as well, for whoever has the conch gets to speak. Like all shells, it deteriorates with the sand and the sun; symbolically, as it deteriorates, so does order and discipline and civility on the island.
The pig's head on a stick, also known as the Lord of the Flies, wieldsa different kind of power. Jack uses the sow's head to control his hunters. He tells them they need to leave a sacrifice which will appease the beast and keep them safe. There's absolutely no truth to this claim; however, the boys want to believe, so it works. I think of it as kind of a placebo--if the patient thinks the pill is medicine, it has the power to heal.