Usually most things ‘raw’ are perceived as being much better and healthier. In the case of sugar, not so much, ok maybe just a little. Raw sugar is less processed then refined sugar, so it still has trace minerals and nutrients present. Refined sugar is devoid of all nutrients. Also when sugar is refined and processed, I read that there are said to be harmful ingredients that are added to it, such as Phosphoric Acid, Sulfur Dioxide, and Formic Acid. Unrefined raw sugar does not have these.
So, I would say that it is slightly more nutritious, and healthier. If you plan on eating sugar I would definitely choose raw unrefined sugar-but at the end of the day, the calorie content is similar as is the overall effect on the your body.
Also, be aware that unrefined raw sugar is different from brown sugar. Brown sugar is sugar that has been refined and then molasses has been added to it.