They are very interchangeable. If there is any difference at all, it's "the woman", emphasis is more on a feminine quality that has changed.
To me, "what she used to be" has more weight to it. A more serious change. You might say "she is not the woman she used to be, her house was so clean the last time I was there. Why is there trash outside her door?" vs "She's not who she used to be, ever since she got addicted to drugs"
Like I said though, they are actually very close to meaning the same thing.
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