Going back to the original question, in comparison to something like a Z06, in my opinion a supercharged M3 is really composed. I owned a modified C6 Z06 and my supercharged M3 is so much more stable. I’m running an ESS VT2-625 with Michelin PS4S tires in stock sizes and I haven’t had any major control issues. Like others have said, it will have similar characteristics to other 500+ hp cars. If you nail it in 1st or 2nd with too much steering input, you’ll get into trouble. Occasionally I’ve had minor slip in 3rd though slightly curved on ramps but my tires were also cold. If you run good tires, let them warm up, and are mindful of your surroundings it’s a blast.
With respect to drag times, I think it’s more of an issue if you’re 6MT (I am). The DCT cars have posted some great times in the 11s. With the manuals, the problem is that you have to shift a little early in 1st, then again before or at 70 mph, and you really can’t power shift these cars without grinding or rejected shifts so you have to take it somewhat “slow.” That being said, even the 6MTs pushing 600+ hp are fast roll race cars. I beat a Tesla Model 3 performance dual motor and a Challenger hellcat, both of which run 11.7 s.
Ironically, the only thing that made me nervous is the way it builds speed. You don’t get a massive kick like you will with high torque cars (e.g., Z06). It feels like you’re being pulled faster and faster and sometimes it’s actually hard to tell how fast you’re going without looking at the speedometer or tach or outside the car. On a couple of occasions I was going so much faster than I thought I was before a curve I almost ran out of distance to brake properly. But I’ve gotten accustomed to it now. If you want a luxurious, classic car modified to be pretty fast from a roll and capable of taking out 90% of the competition, it’s a great path.
Also see this video for a comparison between stock and supercharged (not me):