I never tried Atkins but the few people I knew that did try Atkins lost a great deal of weight. Only they couldn't stick to it because it was too limiting and when they went off they regained all or most of the weight they had lost.
TSP incorporates everything into her program. I was on WW for at least two years and was unable to shed any pounds after the first 5 or 7. I've been on TSP for about two months and am 2 lbs. away from my goal weight. But even better than that, I don't suffer cravings anymore and I am not constantly hungry. I can have almost anything I want to eat, I just have to watch the portions - but you have "portion control" in any diet. And the food tastes really, really good versus the low-fat, no-taste diet I was on previously.
She states in her book that this program is for a healthy lifestyle rather than a weight loss. I haven't felt better in years - honestly.