For me, the S3 handles 'more than well enough' - to define that, however, is a little tricky (and very subjective) but then I kinda need my S3 to be more than just a go-kart.
Admittedly, I generally don't hoon around that often, being closer to 50 than 40 and frequently with my wife & children in the car, but I have always felt that the S3 has bag of grip, handles in a reassuring and capable manner, and decent road manners (e.g. not skittish, holds a line, doesn't need to be wrestled with/constantly adjusted). The power of offer is very decent, and yet is contained within the car's handling capabilities - crucially, this is for road use, where there are other vehicles (often doing daft and/or random things) and not the 'Ring.
Can't say that I have driven the competition - last hot hatch I had was a Renault 11 Turbo(!) and more recent years have seen exec barges like a Jag XF S, and a CLS 350 - but I guess what I am saying is that, for me (and I suspect that is quite similar to many/most(?) other S3 drivers) the S3 is a perfectly suitably handling car, which does an excellent job of getting me from one place to another suitably quickly