South Beach allows carbs, but low GI type carbs once you get onto phase 2...but Phase 1 is really difficult for a carb craver as Atkins.
Except, you are allowed nuts and a serving of yogurt, I think it is?
Once you are on Phase 2 you are allowed to slowly add in carbohydrates to a level that you can handle and still lose weight. For some that may mean one or two carb servings a day, for others 3 or 4. But-all good carbs such as fresh fruit, brown rice, oatmeal, etc.
If you can make it to Phase 2 South Beach can be very bearable and healthful-but if you can't go through the Phase 1 part of South Beach, then low GI may be better for you.