I've heard that before. The reasoning is, "White sugar is more 'processed' than brown sugar, so it's not as healthy." Is this true?
Brown sugar is often "more processed" than white sugar:
Brown sugar is a sucrose sugar product with a distinctive brown color due to the presence of molasses. It is either an unrefined or partially refined soft sugar consisting of sugar crystals with some residual molasses content, or it is produced by the addition of molasses to refined white sugar. Brown sugar contains from 3.5% molasses (light brown sugar) to 6.5% molasses (dark brown sugar). The product is naturally moist from the hygroscopic nature of the molasses and is often labelled as "soft." The product may undergo processing to give a product that flows better for industrial handling. The addition of dyes and/or other chemicals may be permitted in some areas or for industrial products.
C&H has nasty things to say about brown sugar prepared by treating white beet sugar with molasses:
If cane sugar is not specified on the label, the sugar may be beet sugar. What beet sugar makers call "brown sugar" starts out as white sugar crystals that are then sprayed with a brown coating. Often the center of the crystal remains white and the brown molasses coating can be rubbed off in your hands. Not exactly what you want when you go to the effort of baking something fresh from scratch!
Brown sugar and white sugar are both crystallized products. Even in the unlikely circumstance that repeated crystallization removes some essential goodness from the products, you cannot point to one or the other and say with certainty which product has been crystallized more times. Sometimes it's the brown, sometimes it's the white.