In 52 days, I've lost 26lbs following the Atkin's plan. I don't know what the average loss per week is for either plan, but either way you lose more in the beginning & people with more to lose tend to start off faster than those with 5-10lbs to loose. Each person is different and so are their dieting needs. If you haven't read any books on the subject, I'd start with The New Diet Revolution by Dr. Atkin's. It will help you understand the benefits of a low-carb plan (like Atkins) versus a low-fat plan (like WW). Good luck with whatever decision is right for you.
God bless,
Amy-Lynne