When Jason Grace wakes up, he's surrounded by friends. He's holding hands with a beautiful girl who says that they're in love, and there’s a boy with a wild grin who says they’re best friends. Jason doesn’t know what’s going on, but he knows he's surrounded by people who care for him and want to help him.
When Percy Jackson wakes up, he's almost completely alone. His only connection is a wolf that seems to be judging his every move as it decides his worth. He's fighting for his life and desperately searching to find a place that would take him in and accept him.
When Jason and Percy were switched, they didn't just have their physical selves swapped. They had their lives swapped. Jason got to believe that someone loved him, and Percy got to experience what it was like to have no one.