The one-side-up, other-side-down axle movement is called articulation, and it allows all four wheels to stay firmly planted on the ground no matter how bumpy or uneven the terrain is. It makes worlds of difference when off-road (under most conditions)

However, you are correct that this would be detrimental to on-road performance and safety. The front sway bar is disconnectable, meaning that when I go off on a trail, I disconnect it to allow the axle to articulate. On the road, I keep it hooked up 100% of the time, and it actually has a significant amount of roll resistance.

I also have the (currently removed) rear-sway bar that can be re-installed if so desired. With both sway bars installed, this will corner flatter than a stock mid-size sedan, and will resist the body roll that can cause a vehicle to roll over.

So, in summary, it offers the best of both worlds with a 3 minute process to either unhook or re-hook the sway bar.

Here is the link to my write-up on how I changed the OE swaybar links to be easily disconnectable, yet still sturdy (as they work just as they did from the factory): http://www.jeepforum.com/forum/showthread.php?t=395512

The only difference is, I have since removed the lower bolt and replaced it with a clevis pin.