I count calories AND eat low carb. My diet is pretty much low starch vegetables, proteins like meat, tofu, or eggs, and some dairy products.
Sometimes I also eat pre-made low carb/high fiber tortillas, or make bready things on my own using stuff like almond flour and milled flax seeds.
I eat 1200 - 1500 calories a day, and have 20g to 30g of net carbs (that's grams of carbohydrates minus grams of fiber, which are indigestible).
Monitoring my calories ensures I lose weight, and eating low carb reduces my overall appetite to a manageable level. I don't follow any set diet anymore, although I learned a lot of great recipes and meal ideas from doing Atkins.