why count one over the other?

From a weight loss point of view, I believe you want to count calories. This determines whether you gain or lose weight.

If you think about it, they make themselves mutually exclusive. 1 gram of fat counts for 9 cal, while carbs and protein only count for 4. So, if you count the fat, you are going to keep everything down, but in my opinion, I'd rather count total calories, so that it makes for a more complete picture, you know? Besides, if you count fat grams, then you might try to stay under too much, and you DO need fat to be healthy, and to LOOK healthy (i.e. skin and everything). Don't know if that helps, but it's how I look at it

It really is kind of tricky. Let's say you eat 1500 calories a day, but those calories are made up of white flour, high sugar fruit juices, white potatoes, etc. You're not going to be losing weight like you would with the same 1500 calories made up of stone ground whole wheat products, high water content vegetables like bell peppers, celery; fats like extra virgin olive oil; a couple slices of orange instead of a glass of juice, etc.

Check out the Sonoma Diet website for tips on great foods to eat. You can sign up for their emails without signing up, and will get some great tips and great recipes to boot.

Beepower put it quite well.

I'd like to add that the reason you will have an easier time losing by eating the right amounts of nutrients is that if you eat the foods in the first example, you'll probably still be hungry after a day of 1500 calories and your body will actually MAKE you eat more by giving you tremendous cravings for more food, especially sugars and fat. However, if you eat the healthier way in the second example, the fats and whole grains will help you to feel fuller for longer, and you'll be less apt to get hungry, and 1500 calories might be totally satisfying.

You'll still loose weight if you're over or under on fat as long as you're not over your calorie limit, but eating a good balance of fat, protein, and carbs (don't forget fruits and veggies!) will help make it easier to stick to your calorie goals. My advice is to count calories, but use the fat/carb/protein limits more as a guide - if you're slightly over or under on one, no big deal.