I think it depends on what you're looking for in a low carb diet. If you're looking for the benefit of a ketogenic state, go for something on the "very low carb" side and do Atkins. This is best if you think that a diet consisting mostly of vegetables, meat, healthy fats and cheese, etc.--eventually adding in lower G.I. fruit (berries), legumes and beans and (depending) some fibrous whole-grain products is for you.
South Beach and The Zone are both also fairly low carb, and have different approaches.
All diet plans work, and all low carb plans work--the key is "can I stick to this for the rest of my life?" If the answer is no, then it's not for you.
If all you want to do is reduce your carbohydrate intake, then I'd cut out sugar (and sugar-like things such as honey and fruit juice) and refined carbohydrates (most bread and pasta). Instead, I would eat a lot more fibrous non-starchy veggies and fibrous fruit. There are variations of how low carb you go--all the way from a ketogenic diet (0-30g carbs per day) to up to 40% of calories from carbs is considered "lower carb" than the typical American diet.