I'm going to disagree on two things thus far.
1. You won't notice better (than stock) quality dampers on the street.
2. You won't notice a better quality ride with an upgraded Panhard bar.
Let's do this in reverse order. I have an `06 as well, and the stock panhard sucks from the factory (bushings are way too soft). I live in an urban area where we have less-than-perfect roads. Driving around here I would feel the rear step out sideways on uneven expansion joints (highway) and potholes (city streets). The first mod I did was a panhard and it was instantly better under these conditions...not just a little better, but vastly better. The rear was much tighter and no longer felt like it was skipping around on me.
Now shocks. Thinking that superior dampers won't have an impact on the quality of street driving is just flat false. Really false. There's so many reasons/ways to see this is scary, but let's stick with actual experience. We'll do my own first.
Driving my car before and after the Koni Yellows went on was an eye-opener in terms of how stable the car felt (mostly highway driving for me at that time). The Yellows are a nice entry level shock for performance, and they make for a great street damper. I've stepped up from there to Penske racing shocks and it's crazy how much better they feel on the street over the Koni Yellows (to be fair, there's a bit more going on up front on my car since the Yellows were on, so some of the improvement can be attributed to non-shock upgrades). The point is that moving incrementally up the shock food chain shows benefits on the street in ride quality just as much as in performance.
Now other folks' experiences. I've driven SGD's car w/its AST 4100 shocks (a coil-over package). Even with his stiff spring choice, the car's ride quality feelt superior to my old Konis. Keep in mind, when I say "ride quality" I'm not talking about how "comfy" the car feels (Dave's car is NOT comfy on the street). I'm talking about how well put together the car feels - how well you can feel the car take to a road with all its components working in better unison. Nothing's floating around, nothings acting out of sorts with other parts of the car. Any `'ole shit dampers can be soft and comfy, but only the higher quality ones bring the spring action into harmony with the springs. You definitely feel this on the street - it's part of the reason why the German luxury cars feel as they do; they've got pretty good dampers on them from the factory.
Back to the S197 chassis, I've also been in a 2011 Boss (mostly track). Great car. The suspension is not fundamentally different from a 2006 in terms of its basic architecture, but the ride is worlds-different from the crap we got from the factory in `06. I was blown away at how composed this chassis is now coming straight out of the factory -blown away at the difference from what mine was like in `06. Virtually every improvement made by Ford since then has been in component quality (better bushings, better dampers, etc.). The only real geometry change I know of has been in a modestly longer rear UCA (but that has a negligible impact on ride quality). The week before my Boss rides I was in a newer M3, and I'll be damned if the Boss wasn't knocking on the door of that car in terms of ride quality.
The point to all this: dampers matter regardless of where you are driving. They don't matter if you don't care about ride quality or don't have the ability to sense it.
From what I've heard, most folks with the experience of swapping to the STR shocks are very pleased with the improved ride quality on the street. Tapping yet even more experience (and my memory), if I recall Sam Strano frequently recommends these to folks in your situation (folks who want a better ride but are not looking to necessarily track their car). Put very-simply, the better your damper, the better it controls the spring, and the better your ride quality will be.
Best,
-j
