I've ran 19" rims for almost 10 years on my S3, even tracked it a few times in between. Basically, by running wider and lower profile tyres on the rear, you increase grip, and with the S3's inherited under steering chassis, the last thing you want is more grip at the back, which increases your turning circle, and makes it handle poor, especially at low speed. I've gone towards a fast road setup in recent years, so ditched the 19s and put some BBS 18s on, and it's much better, especially around a race track.
Comes down to what you want from your car at the end of the day.