I've had several sports cars, and I'd say most would past the "true sports car" test referenced a few posts ago. I've had more Porsche 944 variants than anything else (944T's, 968's). That said......this car replaced an E60 generation M-Sport 535i with straight pipes and tuned to about 380 horsepower. Actually still have it, and took it on a few a couple of weeks ago.
Not really fair to compare it to the Porsches, half of which were race cars with full cages, spherical bearing suspensions, and stupid expensive dampers (as in $5000/set). Those absolutely handled better, but outside of a little bit of time before I caged the first one, no time on the street. The M3 seems somewhat on par with the two sport suspension optioned ones I have driven (M474 and M030 if anyone knows what that means), but it is more firm than the base suspensions. Of course the wheelbase will make them totally different.
Best comparison is the BMW. The M-Sport basically has the M5 suspension, but not the engine. And like I said, no cat downpipes and a tune for about 380hp. And the M3P absolutely feels more firm and go-kart like than the 5. The 5 is a lighter car, 3600 lbs, but the Tesla feels much lighter, and is much more fun to drive. An M3 would probably be a better comparison, as it is closer in size to the M3P. The 5's seats (the multi contour of whatever the option is called) are infinitely better than the M3P's. But the driving dynamics of the M3P blow away the 5.
Comparing it to a ponycar is, IMHO, laughable. I drove several when I worked for Ford, as I used to do engine development up there, most of the time it was for a Mustang engine. Had a 2000 GT. Those are all very, very soft compared to the M3P. I used to be really into Merkur XR4Ti's if anyone knows what those are. Even teh one I had with stiffer springs, Koni's, and PU bushings all around didn't handle as well as the M3P. It may be the best car i've owned to compare, as far as size and everything goes. It was very lightweight, 2900lbs, and I had it up to 330 horsepower. But again, it just didn't compare. Actually, I had a Mazdaspeed6 for a while, too. It may have felt most similar, appointment wise, but it felt very heavy compared to the Tesla, even though it weighed 500 fewer pounds.
I've never driven the Tesla on a track, and I'm not one to drive at twice teh speed limit, so I can't speak to the high speed stability. But for a street car, it is the most fun one I have ever owned, by a pretty wide margin. I'm not big on dual purpose cars, I tracked two of my Porsches as street cars, but generally prefer the safety of a cage and 6 point restraint on the track. So I can't really compare for that purpose.