Is brown sugar healthier than white sugar?
No, not in any way that matters. The nutritional difference is negligible, and treating brown sugar as a healthier choice is one of the more persistent food myths.
Most commercial brown sugar is refined white sugar with molasses added back. Some is less-refined cane sugar that retains a little of its original molasses. Either way, the molasses is what supplies the colour, the slight caramel flavour and the moisture that makes brown sugar clump.
Molasses does contain trace minerals — calcium, potassium, iron, magnesium. The quantities are the problem. A teaspoon of brown sugar contains a fraction of a percent of the daily requirement of any of them. You would need to eat an implausible and actively harmful amount of sugar to obtain a meaningful quantity of any mineral.
The calorie difference is similarly trivial: brown sugar has marginally fewer calories per gram than white, because the molasses carries some water. Around 15 calories per teaspoon against 16. That difference disappears the moment you measure by volume rather than weight, since brown sugar packs more densely.
Both are sucrose, and the body processes them identically. The same applies to raw sugar, demerara, turbinado, coconut sugar and honey — the last two have marginally different compositions but are still concentrated sugars.
Where the choice genuinely matters is cooking. Brown sugar's moisture and slight acidity change how baked goods behave: it produces chewier cookies, encourages browning, and reacts with bicarbonate of soda in a way white sugar does not. Substituting one for the other alters texture noticeably.
Choose on flavour and texture, not on health.