Nutrient composition certainly makes a difference, while still tying into the energy balance hypothesis. Protein, carbohydrate and fats have different thermic effects, or energy requirements to break them down, which means that 1000 calories from each nutrient in isolation will most definitely lead to different energy yields.

I agree with you that nutrition and weight loss are significantly more nuanced than calories in and calories out, but the energy balance hypothesis factors in such nuance.

I would ask a question regarding your omelette example above — which preparation method would be superior for fat loss if they have the same ingredients?