To me her "Fell in Love With a Boy" White Stripes cover sounds like singing in blackface -- the singing style just doesn't sound natural for her.  Mick Jagger singing "Girl With The Faraway Eyes" was a more natural aping of a different culture's style.
Comparing her to earlier young phenoms like Tanita Tikaram ("Twist in My Sobriety") and Kate Bush ("Wuthering Heights", "Man With the Child in His Eyes") who sang with their natural voices, I'm not too impressed.