I'll explain why stiffening a suspension with dampers is backwards.
The spring and the damper do two completely different things in a suspension. Imagine you're trying to design a suspension. You're sick of bouncing over every bump, so you decide to put a spring between the wheels and the chassis (like a horse drawn carriage maybe). Okay, awesome. You've now managed to separate the wheels from the chassis with a spring. The car doesn't crash over every little bump now. Woohoo!
Except there's one problem. Now when you go over a bump the car soaks up the bump but it continues to bounce and bounce and bounce down the road for miles.
Hmm... Let's do something about that.
What if we put a hydraulic sleeve+shaft that would compress with no resistance, but would resist expanding? Yeah... That's the ticket. We can put this hydraulic damper by the spring, that way when the spring compresses to soak up the bump in the road it won't rebound so forcefully. When it rebounds, the hydraulic damper will control the rebound and slow it down so it doesn't oscillate between compression and rebound like it did before.
Hells yeah we've got a sweet suspension now. When the car approaches a raised bump in the road, the wheel travels up quickly, compressing the spring in the process. Then the spring is allowed to slowly return to it's normal height without exceeding it.
This is how a typical OEM suspension works. It will soak up bumps very well with the weak spring (and required weak damper). It will also wallow around in the corners and lean a lot due to the weak spring.
Want to make it perform better around corners?
The easiest thing to do is to stop the car from wallowing around, swaying this way and that. The best way to do that is by increasing the strength of the spring. If you increase the strength of the spring you will prevent the car from swaying so much in corners and you'll have a faster car. Once you increase the strength of the spring you've got a new problem on your hands. That damper you had before used to be strong enough to stop the spring from expanding after compression. Now it's not strong enough so you've got bouncing again. Okay, we know how to solve this. It's time to make the damper stronger. But remember! You're only interested in making it stronger in one direction. The spring should compress without the damper adding any resistance, then when the spring tries to rebound the damper should control that motion. Install a damper that has strong rebound properties and you're back in business.
At this point you've got a car that handles corners much better than OEM and you've given up a little bit of that smooth ride when you increased the spring strength (there is no free lunch remember). The speed with which the wheels react to a bump in the road will be slower and the spring will translate more of that bump directly to the chassis. This is inevitable with this type of suspension. The ride quality difference between these two springs will be perceivable, but very minimal.
Now that we have this sweet handling car we realize it's not enough and we want more. We don't want any bit of roll left in our chassis if we can help it. It's time to do what? You guessed it, we need even stiffer springs this time, with a damper to match that has even stronger rebound control. Again you'll loose some comfort, but we're after the best handling car ever made and we're willing to give up some comfort.
Want things even stiffer? You'll need stronger springs and dampers to control it. Starting to see a pattern here? There is no good way to adjust the stiffness of a suspension without swapping springs and getting a matched damper with little to no compression resistance and proper rebound resistance.
Those are the basics (and I do stress; B-A-S-I-C) of a typical spring and damper suspension. Next up is the backwards way of doing it.
Okay. You may have noticed that there was a lot of spring swapping going on above. That's one issue with doing it the "right" way. Some people are lazy, or poor, or whatever and they don't want to swap springs all the time. Another (bigger) problem with what I've explained is that (for what ever reason) dampers that have no compression resistance and massive rebound resistance are very, very, very hard to make. It's infinitely easier to design and manufacture a damper that has the same resistance to compression and rebound. The further apart you want the resistance of these two directions of travel, the harder it is to design and the more expensive the damper will be.
Let's enter the real world for a second.
People want a suspension that they can change the characteristics of with the turn of a knob. They want to be able to buy any manner of spring and put it on any old damper and have it work. Most of all, they want it to be inexpensive.
This creates the following situation.
Suspension companies want to deliver what the customers demand but they can't work magic. There is no such thing as a cheap, adjustable spring (is there even such thing as an adjustable spring? Air bags maybe?). You're basically stuck with one spring rate unless you're willing to swap springs and most people are not willing to do that. So customers aren't going to swap springs, but they want to be able to change the stiffness of the suspension. Well, it seems in a drunken haze one night someone decided to look to the damper for that stiffness. Dampers are comparatively easy to make adjustable. It's easy to make compression adjustable on a damper. Hell, it's easier to make a damper with stiff compression. So instead of putting in a stiffer spring, the idea is to make the damper harder to compress. This makes it so the car won't roll in corners like the customer wants, but there is a GIGANTIC problem with this.
The damper will only compress at a certain speed, unlike a spring which can compress as fast as you'd like it. This is the huge problem with making a suspension stiffer by making the damper stiffer on the compression stroke.
Imagine you're approaching a speed bump at 40 MPH. With a weak spring, low unsprung weight, and a decently heavy chassis the spring will compress basically the height of the speed bump while the wheel travels up and over the speed bump. The chassis hasn't moved much at all, and the occupant didn't feel much. With the same spring, but strong damper (in the compression direction to stop the car from rolling around corners) the wheel will approach the speed bump but the spring will no longer be able to compress the 5" it needs to in the microseconds it takes for the car to travel the distance of the speed bump. The damper has basically taken over, and will only allow the wheel to travel at a MUCH slower speed. There is a max speed that damper will compress, and it's extremely slow. Trying to make it move faster will not work (that's the beauty of hydraulics). (Keep trying, and the damper will explode before it moves any faster.)
Now you're left with a wheel that can't move nearly fast enough to soak up any bumps because the damper is preventing quick compression of the spring.
I feel like I've gone on long enough with no real direction anymore. I will leave you with this.
Cheap/crappy suspensions have dampers with high compression rates because they are easier to make. This is the wrong way to make a car stiffer. Good, expensive suspensions have very stiff springs but don't feel very harsh because they have dampers that are designed to control the stiff springs, but won't add too much resistance to the compression stroke.
I'm sorry I couldn't make this easier to read. Maybe it would be best if you ask more questions and I answer them one by one.