I think you can kindof look at the LC diets like a spectrum:
Lowest,
Most Restrictive
<----Atkins-----ProteinPower-------SBD--------The Zone------------>
Its not quite that simple, but I think if you look at it that way, and you can assess your own sugar/carb sensitivity, you can pick where on in the spectrum you best fit. Some people get all the appetite suppression and health benefits they need from The Zone, whereas others just can't seem to handle any refined carbs and sugars.
Of course there are others in there, too. These are the Big Name LCers!