Good question, Ed.
I'm not 100% convinced that Hanon is good for very much. There are arguments for and against them. In the vast majority of cases, though, students begin practicing the Hanon exercises - at least book I - before they are able to play any of the Chopin etudes, so in that way, Hanon is not a replacement.
Studying Czerny etudes, on the other hand, is more useful for playing Mozart, Haydn, Clementi, and even Beethoven. I don't think playing Chopin etudes will improve your Mozart as much as Czerny would.
It's important not to play Czerny the way he indicated - still hand, emphasizing movement of the fingers more than the hand. If you study Czerny, you should do so with a more "modern" technique - applying principles of weight, proper arm and hand movement, etc. - because of the difference in the instrument today compared to Czerny's time.
Chopin's etudes are useful for learning Chopin's piano technique, and you can easily find the application of his etudes in just about all his other music. I'm not saying, btw, that they are limited in usefulness only to Chopin's music, though.
I know you and I had a discussion a while back regarding acquisition of technique from the pieces vs. exercises, scales and etudes. Believe it or not, I mostly agree with what you said, and you are better off learning technique from actual music. Where I disagreed was regarding scales, which are important to learn, and practice, at least in the beginning years, and also I was less dismissive of scales/exercises because they are simply another tool at ones disposal