I've read both books.
They are similar in that you can eat meats and fats, but limit carbs and sugars. But, with Atkins, he advocates using artificial sweetners, protein bars and lots of "fake" foods and mixes. The thing I like about Schwarzbein is that she talks about the toxins in foods as well. That means not using artificial sweeters, caffeine, hydrogenated fats, etc. Also, she recommends eating real, whole-foods, not bars and shakes.
I also think her approach is more natural and comprehensive. She talks a lot about exercise and lifestyle changes, not just diet.
Carole