It's low-carb, yes, but quite different from Atkins. Atkins restricts all carbs, regardless of the source. Naturally-occurring fruit and vegetable sugars are fine on this diet. Atkins also ignores things like omega-3/omega-6 ratios, and as far as I'm aware there is no education whatsoever on things like healthy fats (not all oils are created equal) and the nutritional difference between naturally-raised meats and feedlot-raised meats.
Atkins was a good start in reducing the amount of carbs we eat, but there's been a boatload of research done since then and we're finding that it's a lot more complicated than "eat this, not that." All I know is that I feel really, really good eating this way, and I've continued to shed pounds steadily since the initial plummet (I could stand to lose another ten or so).
Most Paleo followers are also very much into exercise and physical fitness, which is another thing entirely. The whole foundation of the diet is based on the natural evolution of people, and the simple fact is that we were created to be on the move. It's not just a diet, it's an entire way of life.