Lord of the Flies, by William Golding, explores the depravity of human nature when it is left unchecked. This is an interesting question because it presumes that both boys have power; while that is true, the power Jack and Ralph each have is not the same and is certainly not equally effective..
Ralph has no interest in being much of a leader at first, though he willingly accepts the role when the boys choose him. When he does have the opportunity to lead the boys, he is powerless to make them do what needs to be done. He tells Jack:
“Meetings. Don’t we love meetings? Every day. Twice a day. We talk.... I bet if I blew the conch this minute, they’d come running. Then we’d be, you know, very solemn, and someone would say we ought to build a jet, or a submarine, or a TV set. When the meeting was over they’d work for ﬁve minutes, then wander off or go hunting.”
Ralph uses his power to try to keep the rescue fire lit, but it is a lost cause; at least one ship passes by the island, and soon no one has even the slightest interest in keeping the fire going to effect a rescue.
Ralph's greatest power is the possession of the conch, which represents the ability to gather the boys. It works at first, but by chapter six,
Ralph took the conch from where it lay on the polished seat and held it to his lips; but then he hesitated and did not blow. He held the shell up instead and showed it to them and they understood.
Eventually Piggy wants Ralph to blow the conch to gather everyone for a meeting, but Ralph is afraid no one will come because he no longer has any power on the island--and he is probably right.
Jack, on the other hand, takes power where he can and uses it for his own interests. He is a bully to his choir, and he is a bully to every other boy on the island in some way. He is mean enough to the choir that they do not want to vote for him, yet they do. That is power. As he transforms into a savage, Jack is consumed with hunting and getting meat. He keeps all of his hunters and actually gets Ralph to hunt with him one time. By the end of the novel, every boy on the island except Ralph has become part of Jack's tribe, either by choice or through threats and intimidation. His power is demonstrated through negative things like mocking, taunting, and violence, but he is able to increase his self-centered power as the story progresses.
The two leaders have a few moments where they are amiable and able to work together; however, the readers have little doubt that Jack will prevail because he has the greater motivation to succeed: his own self-interest. Ralph is a more compassionate and selfless leader, but he is unable to maintain the power the boys gave him when they elected him their leader. Though Jack is not an effective leader, he is effective in keeping and even increasing his power.
In the end, Ralph tried to use his power to make life on the island better and get them all rescued; he was unsuccessful at both. Jack used his power to create more power and to ensure that he got whatever he wanted; he was successful at both.