my car is corolla AE 92 4-door sedan, which DID NOT have an front swaybar or even a rear sway bar. I first found a rear swaybar and it makes the tail less sluggish in cornering.
I waited for two months for the front swaybar, and as expected, it makes a big difference.
Then I mounted a front strut bar. It makes a difference that I can feel for sure. I don't think it reduces body roll in cornering. In cornering, however, I do feel a clearer response from the steering wheel.
The body flex slightly affects the alignment settings in cornering, though temporarily. And this may gives you a brief fuzzy feeling in cornering. The strut bar helps reduce the body flex in the front part of the car, and it thus reduces these changes in alignment setting.