From personal experience with my Challenger and twisty backroad road racing there is a world of difference in handling with a drag radial and a regular ZR rated tire.

Drag radials are "floppy" and allowed the car to "roll" more when agressively pitching it through the corners, to the point of breaking them loose on certain tight corkscrew turns. Not a great feeling when there is several hundred feet to fall if you leave the road!

My Challenger was wearing them on this excursion: http://waywardgarage.com/201/norms-geezer-cruise/