I definitely prefer Tanya even though I don't like the door thing either (I tried it once, dd got hysterical and have never done it since).
Tanya is also a clinical psychologist and she deals with problems in a different way to Supernanny, who in my opinion, just tries to impose disciplinary measures without looking at the wider picture, or only at a very superficial level.
Dr Byron is also kind to parents, she doesn't berate them