These characters share very few similarities with each other. Carlson and Slim do share their power with each other. Both men are from a similar class. Carlson is a mechanic and Slim is a mule driver, both positions are quite equal in status. Both are also powerful characters and men in the novel, but each for very different reasons and in very different ways.
Carlson is insensitive and callous. He is intimidating both physically and verbally. He cares nothing for others' feelings, which actually frightens the other characters to some extent so the source of his power is others' fear. He is so unaware of others around him however, that he doesn't quite grasp the power his actions have.
Slim is empathetic toward others, he is kind, he listens on a plane that is far beyond what might be expected and he understands even better. The source of Slim's power comes from kindness and understanding. He has earned the respect of everyone on the ranch. The men on the ranch look to Slim for leadership. Slim was one of the few who understood the friendship between George and Lennie and the reasons behind George's undying loyalty. Slim was the only person who could comfort George after he had shot Lennie and Slim not only comforted George, but he understood why George had to kill Lennie. Slim knew without ever being told, how deep the two men's friendship ran.