Firstly,my car isn't an RS3,but in terms of power and torque,I think it stands up pretty well,so the tyre has to work pretty hard.
I've used most of the decent tyre options for the car,and one that wasn't even half decent,that being the OEM fitment Bridgestone RE050.
Since then,I've used F1's,PS2's,PS3's,Supersports,and Toyo R1Rs and R888s.
IMHO.....The F1's are a good all rounder,but prone to wear quite quickly,but the Supersports not only last well,but have excellent dry grip,combined with decent wet grip,and a good amount of warning when they're about to let go,both in wet and dry conditions.
They don't need to be blazing hot to get them to work,unlike some of the more track-oriented tyres such as the R1R and R888,and have grip levels which are not a whole lot less than the trackday tyres.
Of course,you won't get the ultimate levels of dry grip that you'd get from R888s,but as an all rounder,they're miles ahead of the F1s.
In everyday use,you may not notice a huge difference,but if you push on a bit,you should notice better overall traction.
My old S3 will load up the tyres and suspension pretty hard,and losing traction with some tyres isn't difficult,especially on poor surfaces,or adverse camber,and we went to a lot of trouble to get the suspension setup working,as well as picking the right tyres to deal with that,and overall so far,the Supersports are the second best tyres for dry use,and best all rounder.