brown sugar contains molassas which changes the flavor
carb drops are pre-measured. 1 drop = a certain CO2 volume, so you can carb to match the style.
white cane sugar is often used 'in a pinch' when you realize you have no dextrose and the LHBS is closed.
DME is simply a substitute that'll add some more malt flavor at bottling, but not a ton.
different strokes for different folks basically.
Primary: English Mild
On tap: Pale Ale, Lancelot's Wheat, English Brown Ale, Steam Beer, HoovNuts IPA
Bottled: MOAM, Braggot, Raspberry Melomel, Merlot, Apfelwein, Pyment, Sweet mead, Cabernet
Gal in 2009: 27, Gal in 2010: 34, Gal in 2011: 13, Gal in 2012: 10