I've combined the two - taking the best of what I liked about each program and making it work for me. I did that after losing about 75 pounds on SBD alone and lost a good 20 pounds doing it. My cholesterol shot up so I backed off the whole eggs and in six months my numbers were normal again. I went back to SBD and have been there exclusively since.
I find the biggest difference (and I'm no expert because I've never done Atkins strictly) is that you are allowed whole grains on SBD and we tend to eat more veggies and fruit. Plus on SBD you don't have to count anything, not fat, calories or carbs. Induction and Phase 1 (which last two weeks on SBD) are pretty similar. You detox your system of the carbs and then in Phase 2 (which lasts until you reach your goal) you start to add the good carbs back.
In a nutshell instead of being a true "low carb" program, South Beach is a good carb, good fat type program. You might also want to ask your question on the SBD thread. The ladies and gents there are very helpful!