The ratio of rudder movement to tail wheel movement will affect turn radius. The stiffer spring should make the wheel follow the rudder more closely, making the radius tighter. Another function of the spring is to isolate the rudder servo from the shocks transmitted from the tailwheel. The stiffer spring willtransmit more feedback to the servo.

Some setups don't use a spring. They track the rudder exactly, but the servo pays a price, IMO.