A reminder to those who demonize carbs: as Stephan Guyenet points out, restricting your consumption of any category of food--whether you're avoiding carbs, or fat, or meat, or plants--will reliably cause weight loss by removing some highly rewarding/palatable foods from your diet.
So we shouldn't be surprised that both low-carb and vegetarian diets can produce weight loss, and that many people have had success with each method.