Max wins easily. She grew up very blue collar and having to fight for everything while Caroline was a rich kid who never had to lift a finger. Max also has maybe a 20 lb weight advantage and is no doubt much stronger. In one episode, they were needing to look for something in a trash dumpster and Caroline was whining about it and Max just picked her up and unceremoniously dumped her in the dumpster. Max would ragdoll her.