How much difference will it make?

This ^^^^ I know guys that run in the 9s and like how their rear sway bar holds the car. All you need to do is disconnect one side of the front. Especially the larger ones can keep the front from rising and transferring weight.
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Now saying that there are some pretty serious race cars that use a race only design of sway bar. It is used if the body twists excessively. Most drag cars don't use them especially Mopars.
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Damn X frames!upload_2022-2-15_12-2-32.png