The tires handle differntly, namely due differences in tire flex. Radials get much better traction. As I mentioned, the DOT preferrs that the tires with the best raction be on the rear, as it is much more stable, especially in a low traction turn situation. They would prefer that the vehicle hits with the front that spin around and hit with the rear. This even appies with matched tires, new tires are preferred to be mounted to the rear if only 2 are put on.
I know that sounds crazy, especially after years of them pounding in "New tires on the steer axle", which is stil the cae with OTR trucks, but lighter vehicles handle much differently and tend to run higher speeds.

Bill Burmeister