And there we have it. Several points to consider when looking at "awesome results with a Watts install."
1) Bushing compliance. This is particularly true if you go from a stock PHB to a Watts, which will be equipped with either poly or rod-end bushings. Just losing that compliance will tighten up the rear end "feel" dramatically. Between stock bushing compliance and tire carcass squirm, all the other factors are just lost in the "noise."
2) Roll center location and migration: When installing a Watts, it usually winds up changing the roll center as well, unless the pivot bolt is in EXACTLY the same vertical location as where the PHB crosses the axle vertical centerline. Migration of the roll center is indeed an issue, and is what causes the "different feel left to right" that some report with a PHB.
3) Other mods. Generally speaking, a Watts install isn't done in isolation, but is in conjunction with other things, like dampers/springs, control arms (bushing deflection!!), or even a torque arm. So once you throw somebody's entire catalog at the car, what, exactly, is responsible for the effects you observe?
4) Confirmation bias. Let's face it, this is human nature. If you just dumped a thousand bucks and a bunch of man-hours into a project, it's natural to say something on the order of "OMG!!!!1111 It's incredible!!" on a subjective level. On an objective level, there may have been no change, but the perception is still that there was one.
Pros/cons: A Watts is absolutely superior at acting as a lateral location device for the rear axle. There is (+/- bushing deflection) NO lateral shift whatsoever under bump or droop, the axle just moves vertically. A Panhard does move in an arc, which allows some shift to occur. Again, taking bushing deflection out of the equation, and applying the ole Pythagorean theorum, we find that that lateral movement is something on the order of 0.050" or so, not the "INCHES!!!1111" that are sometimes bandied about. So, why NOT go with a Watts? First, weight. The PHB is lighter, both sprung AND unsprung. Second, complexity. The PHB is simple to set up, and stupid-simple to maintain. The watts has a lot more moving parts. Third, price. You can find a nice
rod-ended PHB for around $160, but
Watts links can push past a grand.
I'm honestly not trying to push anybody one way or the other, it all comes down to what YOU want to do with YOUR car. Autocross folks that hit slaloms will feel that roll-center migration a lot more than road-course drivers ever will. And not everybody is running wall-to-wall meat in the rear wheelwells where that slight axle shift can cause rubbing... All I'm trying to suggest is that you think it all the way through, understand what the parts are doing, and then make an informed choice. Nothing more.