To make it really simple as one of the people on the protein power board says: Atkins recommends you start out very restrictive and slowly add new foods to see what trips you up. PP allows you start out more permissive and recommends you become more restrictive if you find something trips you up.
Eat your protein minimum everyday. Less than 40 grams net carbs daily, the calories will usually sort themselves out.

I would agree PPLP is an easier read.