Difference in atkins, south beach, and just winging low carb?

I am on a low carb diet. Not Atkins or South Beach per se, but just not eating any more than 20 carbs total (minus dietary fiber) daily. A friend and I were dicussing this (she is an avid Atkinser). She insists you lose more weight on Atkins than if you just cut out carbs. Anyone have personal experiences to compare?