So yeah here's how you can demonstrate that a shorter swaybar is stiffer than a long one. Take a stick from a tree and break it in half. Repeat this over and over with smaller pieces. It gets harder and harder to break even though the stick isn't any thicker.
How a swaybar works is that when one wheel moves up or down in relation to the other, the bar actually twists and behaves like a spring. One control arm pushes the end link up which pushes the arm on the swaybar up, but on the other side it's moving down or remaining stationary. Whatever one wheel is doing, it's trying to do that to the other wheel. The stiffness of the bar resists this twisting depending on how long and how thick it is and whether it's hollow or solid. This resistance is exactly the same as the resistance from your springs.
If you disconnect your end links and rotate the swaybar you'll see what I'm saying. You'll also see why end links are so anorexic looking. They have no effect on stiffness. I hope this wasn't why you were replacing them!
On the other hand, when both wheels move the same, like if you hit a speed bump perfectly straight, the swaybar has no effect on the suspension. That's the advantage of swaybars. They don't stiffen up the ride in a straight line, only in corners (or potholes, or coming out of a steep driveway at an angle). So to improve ride quality manufacturers like to soften the springs slightly and add a swaybar.
The bad thing about swaybars is that they makes our independent suspensions dependent. They also decrease wheel travel. If you remove the swaybars but replace the springs with stiffer springs to make up the difference, the car will handle better (offroad-like situations especially). But ride quality suffers dramatically. On race track surfaces it's a toss up. The road is so perfect that ride quality doesn't matter and the "difference in independence" doesn't matter; but having an adjustable rear swaybar allows you to change the balance of the car's handling to suit the conditions and the driver's preference.
Here's a paradox for you. Stiffening the suspension DECREASES traction (but reduces body roll). Stupid on a street car. Increase the stiffness and you lose traction and you should not be cornering fast enough that body roll even comes into play. Although cars today are so biased toward ride comfort that a small increase in stiffness is worthwhile if you don't mind the harshness.