To summarize:

From the table above, it is clear that nutrisystem diet is more balanced, preaching moderation in all things. One thing to remember when starting any diet is to remember how long you would be able to sustain it, and be able to function normally in your day to day activities without feeling miserable with cravings. Since you have more variety to choose from for nutri system, in my experience, you would be able to maintain a healthy weight over many years without continuously thinking about being on a diet.
In conclusion, I would recommend Nutrisystem diet plan over Atkins diet plan.