my remapped S3 stronic, runs sweet. plenty of mid-range TQ, infact sometimes I think it's in a lower gear.
the only time I have a delay, is from standing start, but i always thought that was the Haldex sorting out where to put power, it did this before the remap and my old VW V6 4motion DSG did the same.
Normal or spirited driving the throttle response is instant, minor lag if under around 2500-2800 rpm, but that is the turbo, if it's running in 6th @ 40, and i floor it, then the kick down to 2nd takes a little time (0.9 seconds according to the DSG spec.), but then the car feels like it jumps forwards before it launches it's self
mine is a MRC remap, with and ITG panel filter and Bosch F5DPOR plugs, its running around 310/310
there are no DSG remaps for the S3 Stronic yet, some tuners claim they have them but when it comes down to it there not ready yet.
the gearbox will limit TQ, but only at the shift points and this is set to 350nm, the gearbox TCU can also dial-back boost requests from the ECU. so you may not get the full possible boost on a remapped Stronic, but the TQ values are taken from the crank sensor and these can be manipulated to give a lower reading (i.e. multiply true value by 0.9) this 'fools' the DSG/Stonicto allow more TQ through, some reakon they are good for 500nm, but who knows the truth I guess some will some won't but that is one of the risks of going from a factory map. but what you get from the map and how safe it it will all depend on your tuner/map/car/you
I spent a lot of time looking in to this and you really need to give the car to a tuner that know what they are doing and can build you a custom map, as the generic S3 map is probably no good for the stronic.