Because the suspension is doing a few jobs it typically cannot do them all perfectly. To answer the (very general) topic question, you need to understand the roles of the suspension. I.e, what jobs is it controlling?

First off, the whole point of inventing suspension was to allow movement over uneven ground. To do this you need the wheels to be able to move vertically and the best (and cheapest) way to control this is with a spring. The stiffer the sping, the less movement you can do. So here softer is better.

Second. By introducing sprung corners of the car, you have "decoupled" (though not completely) the movement "light" mass of the wheels from the "heavy" mass of the chassis. This allows the movement over uneven ground without too much body movement which is a plus for comfort. In a racecar, there is also a positive in that the light wheels can follow the road surface without large variations in vertical load which kills grip. However, the siffer the suspension, the more "coupled" it becomes again.

An example? If you jack a car up and pull the spring out you can move the suspenion up and down without disturbing the body at all and its very easiy. Thats completely decoupled. If you put in a very soft spring spring, you could still move the wheel up and down but the body will slightly respond by bobbing up and down and its a little harder to move. Its now slightly coupled. If you increase the spring stiffness to the point its almost solid, when you move the wheel the body will move by exactly the same amount. ...And it very hard to move. That completely coupled. The effort required to move the wheel is related to the contact patch force which the tyre will see going over a bump. To minimise these, softer is better in this case.


Third. Now that we have introduced vertical movements of the wheels, the chassis will now pitch and roll. This is not delibrate, and is often not wanted, but you can't design it out without stuffing up the rest of the suspension so you have to control it. Roll and pitch in itself is not bad, but its the secondary effects of roll and pitch which cause problems such as;
Roll camber (always goes in the wrong direction)
Pitch camber (generally unwanted in any case)
Bump steer (more roll = more bumpsteer)
Delayed response of body movement which means delayed build up of steady state forces in the tyres (not necesarily bad but necessarily complicated)
So, to get rid of these effects siffer is better. Now were stuffed because we have to compromise with the first two points.

Fourth. As mentioned, aerodynamic performance is often critically affected by ride height. As JT said, there is no hard and fast rule but generally roll and pitch stuff up your elements working in ground effect so you can get better aero performance by reducing them. This is the reason F1 run insanely high spring rates. Here again stiffer is better.

Fifth. Another effect of a rolling body is that is allows the rolling forces to be transmitted in a split fashion to the wheels. Because of the non linear characteristics of the tyres, the more you load it up, the less capable it is of moving that additional load (massive oversimplifaction, look up tyre load sensitivity). Stiffen the rear springs, it gives them more rolling load and therefore less grip. Ideally, you want the rolling forces balanced so both the front and rear break away at the same time. The optimum balance is a function of many things, one of them being corner radius. A tight track requires a different roll dist than an open track. Here, stiffer or softer overall doesnt matter, rather its the balance between the front and rear.

Sixth. This is where is all turns to s*** because again there is no clear answer. You can add extra springs (third springs) which operate only in axle heave (both wheels up and down together) to let you run stiff and low to the ground for aero reasons (point 4) while still running soft to minimise contact patch load variations (point 2). But now the car is not so decoupled, but only in the axle heave movement, so you soften your ride (corner springs) to regain mechanical grip (point 1). But now the car will rolls too much (point 3). So you add an anti roll bar to stiffen up that mode while still allowing soft single wheel bump (point 2). Adding the ARB now couples the left and right sides together slightly. This means going over a bump on the left wheel, will put vertical disturbance forces onto the right wheel and hurt its grip (point 2). Now you've stiffened everything up and the wheels no longer move anymore so the car wont go over a bump and youve defeated the purpose of the suspenion in the first place (point 1).

Seventh. Tyre temperature is a critical factor in a racing tyre and you can increase it by putting more vertical load through the tyres (though there are other ways). This increase in temperature MIGHT increase grip (which means its going against point 2) or it might cook the tyre and you loose grip (which means its working WITH point 2) Then your benefit of better temperature could then be lost because the car is now rolling again to much (point 3 and 4), or you lost your balance (point 5) because the mechanical grip has changed on one axle (point 2 mixed with point 5)

Eighth. Then you get real world influences on your choice. I.e. your dampers may not damp well at high stiffnesses so the body movements are not controlled (point 1) and oscillations can cause contact patch force load variations killing your grip (point 2), possibly only on one axle too. So changing the stiffness means your optimum balance is stuffed (point 5) So in this case you will HAVE to reduce your stiffness. Another? The track profile could be exciting natural frequencies in the suspension again killing your grip due to load variations in the contact patch (point 2). You need to change either the siffness or the damping here. You can go stiffer and stuff up your balance (point 5) and reduce overall mechanical grip (point 2), but gain somewhat from an aero point of view (point 4) until you realise your car is a sedan that has no aero so you go softer. This should help mechanical grip (point 2) without the trade off in aero (point 4) but now the car is rolling so much the outside wheels are all pointing in the wrong direction (point 3) and your tyres are stuffed becuase part of them are running too hot (point 7). Also, now you have fitted one million springs to the car to stiffen up all of your troublesome modes (point 7) you now cannot change anything in isolation because everything is now coupled to everything and everything you touch will probably violate points 1-8.

So now, you tell me. What better pull-rod or push rod?

Tim
Not the engineer at Force India