Is brown sugar healthier than white sugar?
Not in a meaningful nutritional sense. Brown sugar contains molasses and trace minerals, but both are primarily added sugar with very similar calories.

Key points
Brown sugar contains molasses
Calories and carbohydrate are very similar
Flavor and baking behavior matter more than trace-mineral differences

Molasses changes more than color
Molasses adds moisture, acidity and caramel-like flavor, which can change texture and browning in baked goods.
Trace minerals are still trace
Brown sugar can contain small amounts of minerals that are absent or lower in white sugar, but the serving size of sugar is small and the absolute nutrient contribution is not nutritionally meaningful.
Added sugar is still the category
Whether the crystal is white or brown, adding it to a food counts as added sugar for nutrition-label and dietary-guideline purposes.
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