In Lord of the Flies, by William Golding, Jack and Ralph are two of the older boys, and they quickly become the two established leaders of the island--one by election and one by force. Both of them are English schoolboys who know how to follow rules and be civilized; however, only one of them will maintain that position throughout the novel.
Though Jack has proven experience at being a leader, Ralph is the one the boys choose to be their leader, despite his lack of demonstrable leadership skills. He blew the conch, so the little boys see him as leader. Ralph graciously allows Jack to be in charge of the hunters, so Jack is appeased.
Neither Ralph nor Jack cares for Piggy in the beginning, though Ralph is certainly more tolerant of him than Jack. Jack's hatred of Piggy only increases as the novel progresses and ends in Piggy's murder. Ralph, on the other hand, comes to appreciate Piggy's wisdom and at the end of the novel, and he is the only one left standing with Piggy. When the naval officer arrives to rescue them, Ralph weeps for "the fall through the air of the true, wise friend called Piggy."
While Ralph consistently tries to maintain order and civilized behavior, Jack is consumed by hunting and meat. While Ralph selflessly works on shelters for all, Jack hunts on his own because he is obsessed with killing a pig. When things begin to fall apart, Ralph grows wiser but Jack grows stronger. Ralph wants to talk and be reasonable, but Jack only wants to use violence and force to maintain his power as chief over a tribe of "savages."
There are moments in the novel when Ralph and Jack are united, such as when they are exploring the island or during the only pig hunt Ralph ever participates in, but they are usually depicted as unable to communicate:
They walked along, two continents of experience and feeling, unable to communicate.
In the end, it is Ralph's consistent desire to do the right things, even when it is unbearably hard and he has to fight for his life, which is in constant conflict with Jack's overwhelmingly selfish desires. When Jack paints his face, we know Ralph (and therefore civilization) have no chance to survive on this island.
The mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness.
While Ralph was a weak leader in the beginning, he grew into an effective leader--which is why Jack hated him so much. Jack, on the other hand, was a terrible leader from the beginning (note how he treats his choir and their hesitancy to vote for him), and he only got worse.
When the naval commander arrives, we get a clear reminder about who Ralph and Jack really are: two scruffy-looking little boys. The officer sees Jack this way:
A little boy who wore the remains of an extraordinary black cap on his red hair and who carried the remains of a pair of spectacles at his waist, started forward, then changed his mind and stood still.
This is not a savage chief of a tribe of savages but a hesitant young boy. The officer sees Ralph in the middle of the other boys (as the other boys were hunting him):
And in the middle of them, with ﬁlthy body, matted hair, and unwiped nose, Ralph wept for the end of innocence, the darkness of man’s heart, and the fall through the air of the true, wise friend called Piggy.
The difference between the two boys in the end, of course, is that Ralph weeps for what has been lost, while Jack does not even appear to know there has been a loss at all.
Ralph's style of leadership is much more democratic than Jack's. Early on, Ralph uses the conch to bring order to their assembly, and to give everyone a fair chance to talk. He also shows consideration to all of the boys, bigguns and littluns alike. He shows genuine concern over the littlun's well being, worrying about their lack of sleep and general problem with nightmares. As a leader, Ralph actively follows his own rules and expectations; he expects huts to be built, so he works on the huts.
Jack, on the other hand, uses his superiority as a hunter to assert himself as a leader. Although Jack is keen to have rules at the beginning of the novel, he does not follow through or keep them. He uses his position as hunter to exclude himself from some of the more menial tasks like keeping watch over the fire or building shelters. In tribal meetings, he frequently downplayed or discounted the ideas of other boys, especially the littluns, viewing them as little more than babies. He favors the hunt over all things, which ultimately leads to conflict between Jack and Ralph when the signal fire goes out.
The main difference between Jack and Ralph's leadership stems from the boys' motivation. Ralph wants to be a true leader and execute the job to his best ability, doing what is best for all the boys. Jack is merely power hungry, and seeks to be chief merely to gain adulation. Jack's attitude toward the rules reveals him to be self-centered, concerned with his own desires.