Sawyer and Jack both represent the opposition against each leader. They were both the antagonists in the book and the show because they constantly strived to take control.
The first similarity between them was that they were constantly challenging the leader. Jack was leader of the boy’s choir so he assumed he must be leader of the group. When he didn't get chosen, he began to do everything to become the leader and replace Ralph. He was power hungry and aggressive, and would do nearly anything to be in control. These are qualities Sawyer also possessed. He challenged Jack at every decision, and would not follow the established system. Another detail is that they both end up taking over the camp. They both decided to take action and overthrow their leader. Jack did this by starting another camp and having them join it for food until he has one large camp. Sawyer managed to take over the camp by stealing the weapons and not giving them to anyone unless they listen to him. Jack and Sawyer weren't completely the same, though. A difference between them was that Sawyer was very smart, while Jack wasn’t quite so, even though he was a child. Jack gave speeches about his wanting to be leader and proclaims it to everyone. He took votes, but they were never successful and he never got elected. Sawyer, on the other hand, obviously despised Jack, but instead of letting the group decide, he took matters into his own hands. He thought of an intricate plan that was foolproof, unexpected, and would guarantee him the spot as leader. Having a plan and thinking about a certain situation deeply made him much smarter than Jack.