As for Atkins, I'm absolutely against that diet even though I eat a lot of meat. Here's why:
Your brain is fueled by glucose.
http://news.bbc.co.uk/1/hi/health/1368912.stm
Atkins diet is all about bringing your body into a dietary ketosis by denying your body of glucose (carbs). This makes your body use ketones as a substitute fuel instead of glucose.
http://www.ketosis-ketoacidosis-difference.com/
Your brain evolved to use glucose as a fuel, not ketones. So, while I have no grounds to prove this, I believe that ketones are probably not the best fuel for the brain. Why deprive your brain of the fuel it was meant to use? The way I see it, Atkins diet is like putting diesel fuel in a regular gasoline/petrol car.
I'm all for the carby goodness. Everything in moderation. Variety is the spice of life.