atkins
I lost 65 pounds on Atkins (which was all I had to lose) and most of it stayed off easily for several years - until I was hit with a serious chronic illness. I did not gain it all back, even then.
If you are willing to be patient, you can lose all you need on Atkins. Like any diet - loss slows as you progress. Like any diet, exercise helps a lot.
You will not gain it back as long as you are willing to keep your carbs moderately low. Depending on your weight, gender, metabolism and activity level - you can maintain the loss on 60 - 200 grams of carbohydrate a day. The average American intake is about 300-350 per day.
As a relatively small woman who did strength training 3-4 times a week, I was able to maintain on as much as 100 grams per day and a low-carb day once a week (-30 grams).
If you work out and are pretty active, after meeting your goal you can maintain by just avoiding sugar and high GCI carbs. You may need to "tweak" as you go, doing a week or two of induction every couple of months, or whenever you find yourself putting on a couple of pounds.
You WILL gain all the weight back if you go back to a diet of sugar sodas, breakfast cereals and pasta and potatoes.
Fawn