I wouldn't go so far as to say Cady 'won', necessarily, but...

...he surely succeeded in bringing Bowden "down to his level" (for lack of a better term). Bowden is not only a law abiding citizen, he makes his living with the law. My assumption is that this is a man who holds the law in higher regard than do most of us, it's instilled in his beliefs. But he goes far outside the law to attempt to protect his family. Does it make it OK that it's to protect the his wife and child? Cady toys with Sam until he's in the mud with Max, slinging it back at him. A man like Sam Bowdn really needs to go a lot farther than he did to stay within the confines of the law. It really didn't take Bowden very long to drop the "proper" facade when he realizes "The Law" isn't going to be enough to protect them. Cady may not have succeeded in his ultimate goal (taking away what Sam holds dearest), but he surely succeeds in terrorizing them, and there is no "winner" at the end, just a survivor.

My point is, Cape Fear shows the hypocrisies we, as "civilized" members of a society, live with and under. Sam, the "hero" of the story, as it were, while I wouldn't say he's "not much better" than Cady, is shown to be deeply flawed, and a lot closer to The Pit that Cady crawled out of than he'd ever admit. As I believe are most of us. How many fans of CF watch t thinking Bowden was fully justified in the way he acted, since he was protecting his family? But think about it....