Here is a recent trailer for the upcoming Keira Knightley movie "The Duchess," about the 18th century's Georgiana, Duchess of Devonshire. The trailer starts with an image of Princess Diana (who was related to the Duchess of Devonshire), and says the two women were "united by destiny," although the rest of the trailer doesn't show any particularly striking similarities between the Duchess and Diana.
By the way, this trailer gives away the movie's entire plot, so if you like to be surprised you might not want to watch the whole thing. See below for an earlier trailer that leaves more to the imagination.
2012 UPDATE: Sorry, the video of the trailer is no longer available.
The movie is based on Georgiana: Duchess of Devonshire by Amanda Foreman, an excellent biography of the real duchess (who was, among other things, a novelist, a political activist, and a friend of Marie Antoinette).
Here's that earlier, shorter movie trailer I mentioned above:
2012 UPDATE: Sorry, this trailer is also no longer available!
You are right, Cinderella: no similarity whatsoever between Diana and the Duchess (except for the distant blood relationship) but Diana sells, I guess…