I've been a lurker for long enough and I guess this is the perfect time to jump in..
I currently drive a 2011 S4 with the Stasis tune, not the full package. In the S4 tuning world the Stasis package is very similar to Dinan for you guys. A factory matching warranty along with a more conservative tune for a minimal bump in cost.
Also, there is much better value to be had when tuning an S4 by piecing together parts from the variety of aftermarket tuners as opposed to going with the full Stasis setup. So while the Stasis kit is great as a turnkey solution, unless the warranty is very important to you, you can save serious coinage buying individual parts.
As far as performance goes, out of the box the S4 is definitely quick. Not quite M3 quick, but not exactly miles behind either. Many folks have managed anywhere between 12.8 to low 13's on stock setup.
One thing to keep in mind is that there are two versions of the Stasis tune out there in the wild. The older version that was coded by APR and the newer file which came as a result of Stasis purchasing one of the other tuners; Revo. The old file was good for probably an additional 50-60 hp, bringing the car up to around 400-410CHP. It may seem like my math is fuzzy but its been proven time and again that the S4 comes underrated from the factory and actually has closer to 360-370 chp in stock form.
The newer version of the tune produces a good deal more power. My car dynoed ~283whp in stock form, ~325whp with the old tune, and ~348whp with the newest version (same dyno). Nice gains for sure.
For comparison sake, a Stage II car, (tune + pulley), put down ~360whp 5 min after my run. Stage II APR cars, as mentioned above have been running anywhere between 11.9 to 12.3 in the 1/4.
As far as comparing it to the M3, it really depends what you are looking for. With the original tune and in a straight line from around 30-110, my car put roughly .5-1 car length on a stock M3 (09'). Once I had the update done, that grew to almost 3 lengths. But straightline speed is where the performance advantage ends. M3 feels sharper, better balanced and is more of a sports car, where as the S4 is more a sporty luxury car. Even with springs, front/rear sways, there is no hiding this car's weight, and the AWD leads to some numb steering feel in certain situations. FYI I do not have the sports diff, which many S owners claim transforms the car. I refuse to try a car with it, as a noticeable difference will ruin my happiness with my ride haha
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I was cross shopping between the M and S4 and ultimately it came down to northeast weather pretty much mandating AWD for me and my driving habits.
Not sure where OP is located, but if near NYC and you want to go for a drive, let me know and good luck!