The Spring Rate controls the transfer of weight of the car. During braking and acceleration the weight of the car shifts forward and backward. Softer front springs aid in shifting the weight to the front, thereby reducing understeer. Softer rear springs allow the weight to transfer to the rear, consequently reducing oversteer. Alternatively, to induce understeer or oversteer, do the opposite and stiffen the corresponding spring rates. Keep in mind that spring rates that are too soft produce a car that is not as responsive as one with a stiffer spring rate. So, you have to find a compromise.
In F1 car, since you want more grip at the rear during acceleration, the spring rates, if hard, resists the weight transfer to the rear, making the rear hard and want to fight back, loosing grip. So we want to make the rear take more weight during acceleration for better grip.
F1 cars have more varied requirements. And, F1 cars seem to prefer a slightly lower front spring rate to reduce understeer.
Taking in account things explained before, spring rates are adjusted according to conditions on the track, race strategy and driver preferences.
In a Forward engined car, since the driving wheels are in the front and weight goes to the back, during acceleration, we make the rear spring rates as stiff as possible to resist the front wheels from loosing too much grip by reducing weight transfer to the rear while accelerating. However, the front spring rates must not be too soft, because most of the car's weight is up the front.