I have done both and lost on both. I stuck with Atkins a lot longer, had tons more energy, and was much less stressed than when on WW. I was never hungry except first thing in the morning when I expect to be.
The one thing I did resent was all the selling of food in the meetings. Passing out samples, advocating snacking on their products, etc. Other than that, I think WW is a wonderful well thought out and medically sound program if you stick to it and eat real foods, not the junk foods.
Any way of eating comes down to just one thing. Are you willing to do or not!
If willing anything will work. Pick the one that makes you feel great and lose weight. Just make sure whatever way of eating you choose is a healthy one.