First of all, hi!
I'm doing Atkins because it's the one I started with and the one I understand the most. When I do it correctly the pounds just melt off. If I cheat, even once, I screw up 3 days worth of being good.
I've never tried CAD or CALP but lots of ladies here have had success with it.
When they make something low-fat, they take all the taste out of it. So, to make it taste better, it has more carbs in it. Ever notice how sugar has 0 fat grams in it, but look at the carbs!
On induction you have to be very strict about what you eat. (Remember that you can't have a small salad until after a few days because veggies have carbs too.) So if you eat low-fat cheese instead of regular cheese, you may get more than 20 carb grams per day. After you come out of induction and start adding carbs to your daily intake, you can eat whatever you want within your range. If you want low fat, read labels carefully and incorporate it into your intake. I was able to get to 85 or so carb grams a day and still lose, but then I COMPLETELY fell off the wagon. I am on induction again, let's hope I can stick to it this time.
Good luck to you in whatever plan you choose!