bias ply tires have the cords running at an angle of 32 degrees from bead to bead. this allows the tread to squirm about causing an instability in the traction the tire can give you. bias ply tires also run hotter because of this.
radial tires have the cord running at a 90 degree angle from bead to bead, stabilizing the tread, giving more consistent traction, and running cooler. when goodyear went to the radial tire at a bristol race in the late 80's, dale earnhardt used the radials, and rusty wallace ran the hoosier bias ply tires. rusty out qualified dale, but dale told rusty, "i will lap you by lap 50. he was close, it was lap 53 as i recall.