Nice write up Warren, as usual.
I think the biggest difference for me was the instant shove the supercharger gave against the turbocharged S3....any revs, any gear, any time, it just picked up really strongly and was never caught in a dip in the power curve....the engine really was sublime as you yourself found.
Mine had the Dynamic ride control and the sports Diff, with the Comfort suspension/diff setting making cruising much more serene than it is in the S3, and improving the handling dramatically in the Dynamic setting, although this also artificially weights the steering too much ( I set the 'Individual' setting on mine to be Dynamic in everything except the steering which felt more natural in 'Comfort' setting )....however, you couldn't disguise the fact that it was still a heavy car and it simply isn't as nimble as an S3.
Mine was also manual, which hit me hard come resale time as everyone wants flappy paddles these days ( playstation generation ) but for me it really added to the experience.
The tuning options weren't available when I had mine as it had only recently been released, but to my mind the car never needed more power as standard, so with a little bit of money spent wisely, it will be an absolute rocketship and be quite capable in the right hands of frightening far more serious machinery.
In summary, the two cars are so different that it is very difficult to compare them....if you were doing a comparison test in a magazine, you simply wouldn't put them any where near each other !
You really need to drive both and then decide what you want from your car, but from personal experience and simply on a personal level, the S4 is the better car and if I could justify it, I would buy one again in a heartbeat ( although I don't think they offer the manual gearbox anymore ) !!