White sugar only lends sweetness, while brown sugar also brings flavor. If you're already using a flavored syrup, the best choice for your coffee is definitely white sugar.
White sugar is also better if you love the flavor profile of coffee and only mind its bitterness. A bit of white sugar will emphasize the coffee's essence but mask its acridity.
Brown sugar creates a deeper, richer, and more complex flavor inside your coffee cup. It blends with the coffee’s prominent notes and will especially shine in darker roasts.