My own take:

DSGs are really just a manual gearbox with 2 differences: one the computer controls the clutch and two, there are two clutch units, one for even and one for odd gears.

Regular automatics use a torque converter to switch between gears.

I'd say automatics are smoother, especially in the lower gears but it seems to sap a lot of power as well. So the car feels a bit more lethargic at low revs.

DSGs tend to be a tad rougher in lower gears. It is after all a clutch assembly. But the gear changes are very very quick (because the other is already pre-engaged) and like manuals, it's usually more fuel efficient than automatics.