PP is very similar to Atkins, and probably provides similar benefits with blood lipids- namely lowered insulin that leads to a cascade of benefits.

The main differences between Atkins and PP is that Atkins has an "induction" level of 20g daily carbs followed by gradually increasing carb levels, while PP starts you out at 30-40g of carbs per day, and you stay there until all the weight is gone. Also, PP requires a minimum amount of protein per day (calculated based on your individual needs- bigger people need more protein) - so we keep track of two macronutrients (carbs and protein) while Atkins only keeps track of carbs.

There are other subtle differences between the two plans but those are the two major ones.