My take on that particular song is that she polished a song that, by its nature and lyrics, was intended to be rough around the edges. That smooth polished performance is incongruous with the content.
Also, Baez singing in a voice that is so feminine does not fit either. I don't have a problem with the gender reversal per se. For instance, on Raising Sand I like Krauss singing "Through the Morning, Through the Night."
Maybe if Janice Joplin had done "The Night They Drove Old Dixie Down" I would have liked it better. It surely would not have been over polished or over produced.
But finally, what really blows it for me is that Baez makes the song over sentimental, almost saccharine. Levon Helms does not. His delivery has pathos and emotion without being sentimental.
Anyway, that's my take. It isn't any more valid than anyone else's.