I think maybe the difference is that the MPDG doesn't have a back story; she's entirely define by her manic dreaminess, here and now, whereas the Wise Fool is the Wise Fool because of Reasons, and the exploration of those reasons is generally a large part of his plot, as in The Fisher King (the Gilliam movie, rather than the legend); Williams' character is there to help Bridges' character evolve, but we also learn about his own story, and there is as much redemption for the Wise Fool as there is for the cynic learning from him.

So I think if the MPDG had a back-story an a journey of her own, rather than being a plot device with no past and no future, it would be rather different.