Both of these characters have different viewpoints of how a leader should carry himself. Ralph wants the island to be democratic and most important he wants the boys to be civilized. Jack on the other hand wants to run the island in a completely different way.
Jack wants to use brute force and uncivilized ways to survive on the island. In the beginning of this novel you can already see Jack and Ralph competing for leadership. As the decision of who will be chief was going on you see Jack saying “I ought to be chief…..Because i'm chapter chorister and head boy. I can sing C sharp” (15) You can see by this that Jack wanted to his accolades in choir to show up