Dietary fat is more easily converted to body fat than are either carbs or protein, but the type of fat you eat also plays a role. Raw fats (like those found in avocado, raw nuts---which should be soaked before eating to deactivate enzyme inhibitors--and olives) contain within them the enzyme lipase, which helps with digestion of fat, while cooked fats (any heated over around 118 degrees, including most vegetable oils) are denatured and have had their enzymes destroyed. Coconut oil is even supposed to help your body burn off fat.
As for what kind of "diet" to follow, I think focusing on just one nurient (fat, carbs, isolated vitamins, whatever) is a somewhat erroneous approach. Instead, if you stick close to what nature intended for humans to eat (foods that the human body can easily assimilate) you don't have to worry so much about counting anything: fats, carbs or calories.
Try increasing your intake of raw foods and decreasing (or, better, elminating) processed foods, including most vegetable oils (the exceptions being first-cold-pressed extra-virgin olive oil and raw coconut oil).
Sticking to a diet of about 55-65% healthy carbs (from fruits, vegetables, legumes and grains--limiting the amount of wheat and rye), 20%-30% fat and 12-20% protein is a good guideline. This can not only help you reduce body fat but, perhaps more importantly, is a health-promoting way of eating, based on nutrient profiles of healthy populations, and that can reduce the risk of many diseases that are rampant in the US, rather than just working on appearance.