I spoke to the Bilstein rep at Audi Driver International and he said it's the dampers that are the biggest issue with some Audi models, they have very little compliance and run way too stiff. Supposedly they make the biggest difference to ride, it's just you still need springs to get rid of the 'speed boat' rise at the front end.
It is for definite the dampers and it is crazy why AUDI, especially in the face of years of criticism, would continue to fit poorly spec'd dampers. People slate the S-Line springs for being crashy or the Sport for being bouncy; it is all to do with the damper. If you put a Bilstein Sprint B8 damper on an S-Line or an S3 it would transform the car.
The Sport dampers off my TDI are crazy stiff in "bump/compression" but have hardly any rebound damping (which is where most damping control come from). Essentially what AUDI have done is created a falsely stiff ride because the car "rides" on its dampers and less so the springs and it makes the car feel out of control sometimes as it struggles to retain the body from bouncing up. The S-Line dampers are the same as the Sport, so the stiffer springs and stiff bump/compression dampers can give an unsettled ride and one that lacks composure as the car floats and nods at the front end over dips and crests. Having said that I have fitted some S-line springs to my car and the ride felt barely different to the Sport springs, albeit on better SACHs Advantage dampers.
I have now recently fitted S3 front springs and the car still rides ok on aftermarket SACH Advantage dampers, despite the S3 springs being shorter are stiffer than the S-Line springs. So you can massively change the spring rate and still have a similar ride.
An alternative to Koni FSD would be Bilstein Sprint B8 dampers - I have these on my BMW and they are a very very good sports/road damper, not crashy but well controlled ride. I wouldn't recommend the SACHS Advantage 40023 (rated for all 55mm strut cars including the S3), although I have them, as there still isn't enough rebound on them to give the well-damped control you expect and it does occasionally lose composure and bounce, but they are an improvement over stock Sport/S-Line dampers.
The stock S3 dampers are pretty short, but the valving is not stiffer than the Sport damper, perhaps a touch softer on bump/compression and slightly more on rebound so they are not as "bad" as the Sport/S-Line dampers.
The rear dampers are ok on A3s IMO, the damper is as you'd expect reasonable bump and good rebound, it's just the front that are the wrong way round.
The problem with coilovers for me is that there is too much to fiddle with! and probably always fiddling with it!