While I agree that the original box is a great collection of Billie Holiday's wonderful music, I don't like the mastering. I was disappointed by the sound quality; Billie’s voice and some of the instruments at times sound harsh and piercing to my ears. Judging by other issues of some of this Sony-owned material, such as the excellent Teddy Wilson CDs with Holiday on the Scottish Hep label, which were mastered by the late John R.T. Davies, I think the Sony mastering could have been better.
Just a guess, but maybe the mastering engineer decided to boost the higher frequencies to make the sound more detailed and transparent. This is done quite often these days and many times the result is what I would call a "shrill" sound. Many people seem to like it, but I don't.