I own both, drive the GT500 on nice days when I don't have to pick up the kid. Mine is an 08 vert so its probably one of the crappiest handling GT500's you could buy, but I didn't buy it to track it. It rides nice, handles good enough for the road. My only complaint is traction, something thats addressed in the 2011 model.
It doesn't feel as tight as the M3, nor would I expect it to. It's raw brute power thats just a kick in the pants to drive. My M3 is the daily driver, kid seat in the back, and I can't think of a more perfect car for that. The Shelby is my fun car, driving out on my own, top down, ford racing exhaust blaring and a shaker 1000 to blast tunes. I get the best of both worlds really.
This isn't to say I don't like the feel of the Shelby. My family is into old cars, my brother has a 69 Camaro SS 350 vert, and my old man has a 59 Thunderbird with the factory optional 430ci. The Shelby just captures that modern muscle car feel that's unrefined, simplistic, and snap your neck powerful.
Sometimes I chuckle at some of the M3 owners on this board that idolize a stripped down M3. If simplistic performance is what your after, the M3 is the wrong choice. For the money, the GT500 fits that "feel" bill far better, and its one of the best 6 speeds I've ever driven, especially after I dropped in a Shelby short throw shifter which I think is part of the comp package for the 2011.
08 GT500 convertible red package (Black w/ Red stripes) /Ford Racing Exhaust /Cold Air Induction 560hp
10 Porsche Cayenne GTS Black w/ Black Wheels 408hp
11 M3 Silverstone w/ Silver Novillo Leather /Tech /Premium /19" /DCT /Ipod 414hp