The major difference is that Atkins just says "eat all the meat you want, don't care about fat. Cut out carbs to a net amount of 60 (if I remember) grams a day, lower in the induction phase."
In Why We Get Fat, Taubes focuses specifically on the insulin reaction to what you are eating and calls out sugars, High Fructose Corn Syrup, refined flours and breads and other liquid sugars as what is making us fat. He speaks to insulin resistance in muscle and liver cells, and the body's reaction to caloric "starvation" type diets.
He doesn't suggest, as you say in the previous post, that you "limit our carbs to leafy greens". He says that if you are obese, then losing weight will come from a diet of protein, fat, and leafy green vegetables. This is different from saying "ignore all carbs but leafy green vegetables".
Again, the focus is on the reaction of the body (and every person's reaction is different for a number of reasons - all of which he discusses) in terms of insulin response and chronic diet issues.
