Brown sugar is sucrose, just like white sugar. Brown sugar may have had less processing than white, although this does not affect the nutritional value, or it may be white sugar to which molasses has been added to change the color and flavor. Raw sugar is also sucrose, just like white sugar. Raw sugar is just less refined than white sugar, but again this does not offer any nutritional value. Sugar in any form is not a good source of vitamins or minerals.
Honey offers no special health benefits.
Honey contains two simple sugars, glucose and fructose, which are the same two simple sugars that combined make sucrose or table sugar. The body uses them the same way, no matter what the source. These sugars have the same caloric and nutritional value. The largest difference is in the price and distinctive flavors. If you enjoy the flavors, these sugars are probably worth the extra expense.