I've had both. The old S3 was one of my favourite cars for all the positive reasons stated so far. Mine was one of the first - before they raised the ride height - and it handled beautifully, albeit a bit softly, with a little understeer on fast, tight corners until the Haldex cut in. The only problem was that it bottomed when pressing on, on bumpy roads.
The new S3 has a delicious engine, slick gearbox and good handling on smooth roads - more neutral, and the Haldex appears to cut in earlier. However, move it onto a bumpy windy road at speed and the body control falls to pieces, and the anti-lock braking light flashes away. Interestingly, I think it goes beyond this. I have driven three S3s on the same 2 hour/road drive on different occasions in the same weather conditions. The first one was superb and I placed an order. My own handles as I have already described and so I complained to Audi. They gave me a third one, a demonstrator, to drive and it was terrible! It bounced all over the same stretch of road. It made me appreciate my own car better (for a short while!). So, my advice would be try the car you want to buy on a bit of typical B road that you know well. It it shapes up, buy it. If not, try another....
Incidently all is not lost, after feeling increasingly frustrated about spending all that money and just using the new S3 to go to Tesco or on the motorway, I have just had Bilstein adjustable dampers and coils fitted, and I now have a car that handles like the one I first roadtested, albeit with a bit of a firmer ride.