I don't know how you'd get an S197 setup to where it could handle "better" with no rear swaybar, unless it was really screwed up to begin with....
Swaybars or anti-roll bars are very useful things, and removing them completely is usually a desperation move to fix other issues. Most racers I've seen running without a swaybar are usually REALLY BAD at chassis setup.
Even Formula1 cars use anti-roll bars (the "T" bar above) at both ends, and they have a 3rd one called a "FRIC", or "Front to Rear Interlink" (read more
here). Where an anti-roll bar limits "roll" side-to-side, the FRIC system limits dive/heave front to back. F1 does not "make" the teams run anti-roll bar setups. They do it because IT IS FASTER. Do you think some Mustang internet expert has this stuff figured out better than these teams??
But hey, I'm willing to test anything. And yet when we have tested swaybar stiffness on our S197 car at more than one dedicated test day, and let the clocks decide, swybars always ended up being necessary for the fastest times. At the event above I had the Vorshlag crew adjust the bars and then I'd make laps on an easy-to-drive course. Come in, check the times, make more adjustments, drive more. After hours of this testing, the swaybars ended up at full stiff on BOTH the front and rear, which was the fastest setup. And we had 450F, 175R #/in coilover springs and monotube adjustables. We obviously needed more spring rate... (ended up at 800/350)
Most of the folks discussing swaybars for Mustangs on the internet are running around on craptastic lowering springs, bottoming out their OEM length struts, and have worn out tires that were no good to begin with. Their test conditions, data measurements, and setup is very probably "less than optimal". Take your advice.... carefully.
Be skeptical!
What I'm saying is - don't take anyone's advice as "solid" that you don't know personally, that tests scientifically, and that is fast. Of course every spring/shock combo on a given chassis might take a unique swaybar stiffness to be ideal. But running "no rear bar" is almost always a bad idea. I've
tested this on numerous chassis and usually end up with larger than stock, adjustable bars at both ends.
Swaybars are a big, dumb piece of steel. There's not a lot of "Technology" in the design, and I usually don't care about brand-to-brand differences. I'm not saying there is any perfect swaybar, but I do like the Whiteline stuff for their large range of adjustment plus the added inboard wheel room in the rear. Sure, its solid so it isn't as light as some bars out, but on a 3600 pound car like the S197, the miniscule weight differences in swaybars becomes pretty moot.
If you cannot afford to do a dedicated and timed test, with a course simple enough to take out the "Driving variable", then trust someone who has done this for nearly 3 decades. Get adjustable bars at both ends, bigger than stock. DON'T use a big swaybar as a crutch for lack of spring rate, though, just for tuning and roll control. Have someone take pictures of your car loaded up in corners and look at the relative lean you have. It should be under 3 degrees or so, otherwise you are putting too much load on the outside tires and giving up mechanical grip.
Good luck, and stay skeptical!