Yeah, that atkins thing is very interesting!
I did atkins for a few weeks before, and I lost loads of weight, but I put it all back on, super fast. It definitely puts you in ketosis! I definitely prefer LT though, because it eases you off LT, and Dr. Atkins considers the Atkins diet, a diet for life, permanently low carb. I love that you can break the psychological barrier to food on LT, and I feel so much more energetic on LT, than I did eating meat constantly.
That said, I was just using Atkins as a quick fix, with no long term plan. Now LT is my route to Low GI/GL.