It still comes down, which they even admit on the atkins site, that weight loss comes directly from calories in vs. calories out. And one of the things they tend to reference is the low fat/low protein part of the calorie restricted diets that they claim are worse than Atkins. I don't think any diet on earth ever said to get the majority of your calories each day from sugar, so yes, if you eat a high carb, low fat/low protein diet, you're going to feel hungry because you are consuming sugar primarily. This is difficult to maintain and also clearly unhealthy.
Atkins isn't a bad way to go about things, but it is still trying not to focus on calories, which gets into pseudoscience range because the science directly states that calories in need to be less than calories out to lose weight. It's just a decent way for sedentary people to avoid drinking sodas and eating a loaf of white bread each day and lose weight, and I totally agree. But a more balanced approach is going to be easier to stick with by far, in my opinion. Not a "high carb" diet that they keep comparing things to, but not a no/low carb diet either.
After having read that website, I had to go read some unbiased crap to get actual answers. The only diet they compare atkins to on the website is the mythical "high carb" diet that they think people are doing. I'd be much more interested in seeing some baseline studies comparing low carb vs. balanced. And they did! And there was no difference apparently.
Effects of 4 weight-loss diets differing in fat, protein, and carbohydrate on fat mass, lean mass, visceral adipose tissue, and hepatic fat: result... - PubMed - NCBIand
Effect of diet composition and weight loss on resting energy expenditure in the POUNDS LOST studyspecifically states that all benefits that might show up were basically gone after a year from choosing one type of dieting scheme over another.
In summation, it doesn't matter what fad diet you try, as long as you stick with it. You'll lose weight if you consume less total calories than you expend each day, regardless of the means. Atkins isn't bad, but it also isn't really better than anything else that has you eating a balanced amount of macronutrients and keeps your calories under your outgoing usage. Drinking all your calories each day from sodas would be retarded and anybody doing it and "counting calories" is a retard. Or a Body Positive Advocate.