The transfer method to the base metal is one big difference. Mig's main way is short circuit and dsfc main way is spray transfer. Mig welding can be loud with the wire shorting out and "exploding" constantly. While dsfc welding can be much quieter more like a hissing sound.
Shirt circuit can lend itself to problems like lack of fusion where dsfc with flux in the process helps to avoid this among many other things.