Hmmmm...I am one of those people who failed on strict Atkins (yes, I've read the book -- more than once --and yes, I followed induction to the letter). At first, eating formerly forbidden foods such as real butter and mayo, and cheese and meats was very freeing. But I just didn't have much energy as time went on, and my weight loss wasn't that great. So I modified things. I truly believe that for most of us, eating "clean" is the best solution. It doesn't require cutting out whole groups of food, it's healthy, and it produces results (my stats are an example). Shopping the outer perimeter of the store, eating real fruit, veggies, good meats (not stuff smoked in nitrates), good dairy, good cheese, and some nuts, is the way to go. I don't completely cut out breads, but I consider it an extra, not part of my clean eating plan. And obviously, garbage foods are verboten, although I occasionally partake.
Having said all that, these last 15-20 pounds are REALLY tough to get off! It's now a matter of vanity, not health, since my BMI is <25. But it's important to me to go all the way down to my ideal weight. So I currently swing back and forth between different plans, all the while keeping my protein levels high. I do pay attention to calories, because I'm small enough now that too many cals results in weight gain for me (whether or not they are LC cals).
The happy news is that losing weight has resulted in far more energy, and stellar bloodwork. I was fortunate enough to have pretty good bloodwork even at my heaviest (no diabetes, etc), but it is even better now. My LDLs are 70, my triglycerides are 70, and my HDLs are 63! It is such a joy to see all the good numbers. I am probably healthier at age 44 than I was at 30. Yippee!