My experience was very positive. I have suggested it so several people, and those who tried it are still on it. Atkins is similar, but not the same. The paleo dieter avoids processed foods, and Atkins can include lots, they even sell them.
The main positive effects I saw were, reduced # of headaches, much improved digestive health, and reduction of aches and pains. I had an old athletic injury to my knee. After about 6 months on the diet the pain disappeared, and has not returned. This surprised me, because knee injuries rarely heal completely, and I had pain for nearly 20 years.
I also saw allergy symptoms much reduced. I believe that all of these are related to the reduction in inflammation you get once you stop eating inappropriate foods. Wheat is the primary negative. I have several Hubs that touch on diet.