The behavior is the same for both open and closed wheel cars.
Main use of antirollbars is to reduce the body roll of the chassis while turning.
A stiffer rollbar on a particular end will produce less body roll and usually will provide less mechanical grip at that end. In this way you can control the "balance" of the car while turning.
- Stiffer front than rear will result in an understeer behavior while turning.
- Stiffer rear than front will result in an oversteer behavior while turning.
On some cars a stiffer rollbar will produce less dynamic wheel camber change. So if you soft a particular end of the car you may have to decrease the camber (more negative camber) on that end.
Stiffer rollbars will make the car feel more reactive to driver input, will feel more precise, but it will reduce the grip, make it feel also more "slidely"
Softer rollbars will make the car feel more "spongy" less reactive to driver input, but will provide more grip.
As always on car setup, is a matter of "compromise". You cannot go to soft or to stiff.
Also, front and rear wings will affect more car balance at turning at high speeds compared to what the antirollbars do.
Another factor to consider is your driving style. If you prefer a stiff (understeer) car or a loose (oversteer) to drive.
I am sure I may be missing something and someone will be able to complement this, even correct something I may have said.