I don't like fermented out brown sugar or molasses, but some people do. To me, when the "sweet" is gone it leaves behind a weird non-sweet molasses flavor. Molasses is bad enough (hate the stuff!) but a not-sweet molasses is really odd to me.
You can use any type of sugar in wine- white sugar, honey, maple syrup, turbinado sugar, piloncillo, molasses, fruit, etc.
Most delicate fruit wines wouldn't taste very good with deeper flavors, but honey is nice because it leaves behind a faint note of honey after fermentation. I use honey in my crabapple wine near the end of fermentation to "smooth" it out. (Recipe posted in my recipe pull-down under my avatar).