I've done both, and WW worked better for me (though it wasn't what worked best for me). However, that was the old WW, the "exchanges" system, not the new "points" system. From what I've read, I feel that the new system wouldn't have been as supportive of my weight management efforts as the old system was. With Atkins, I was in that 10% minority that actually react negatively to Atkins, and had my cholesterol shoot up on it. As long as you take all the recommended vitamins and supplements, and get a few blood tests over your first six months, Atkins is worth looking into: If you're not willing to pay for all that extra supplementation and periodic testing, then perhaps WW is a better approach for you.
In the end, neither approach will work for you if you're not able to completely change your lifestyle, permanently, to match that needed for the approach you choose. For Atkins, it means substantially reducing or eliminating bread, pasta, potatoes, corn, fruits, and sugar from your diet. For WW, it means substantially reducing or eliminating butter/margarine, oil used in cooking (even when eating out), big steaks, hamburgers with all the trimmings, etc.