I've noticed in basic A3 if you want the maximum performance, better keep the gearbox in S auto mode and let the car shift when it's optimal. If you do manual shifts, there's usually lag in gear changes, the car seems to need a short moment to think "oh you want to shift now, ok let's do this". I usually use manual shifting only when I want to keep the specific gear, and there's rarely need for that. I know that's boring in a way, when it's sportiness what you're after when you shift manually.
Would be interesting to know what's the RS3 like. But I wouldn't compare Audi S cars to BMW M cars, but maybe to the regular models with the additional M.