A tuning box will never get as much out of the engine as a remap, neither will it ever be as economical if that's your bag.
Essentially they adjust the signalling to the boost pressure sensor and fuel rail sensor so that the ECU gives more fuel and boost in relation to what the base map actually dictates. They are more sophisticated than the old variable resistors of old, and they have a degree of intelligence over how they provide gains at any particular point on the throttle curve, but like I said earlier, a remap will give you more.
I've got a DTUK box on my A4 as I wanted a solution that was removable, but now it's out of warranty I'd get it remapped properly if I were keeping it.