I drove an '06 Mustang GT for a year. The live axle was absolutely not "very noticeable."
Yes, there were certain corners where it was noticeable to someone who knew what to look for, but 95% of the time you just can't push the car hard enough on public roads to trip it up, and even when you do it's minor skittishness. If you're driving at 9/10ths on a public road, you're an idiot. And if you're doing that on a track, the surface is going to be smooth enough to where it's just not a big deal.
As far as the average driver ever being able to notice a difference, you're VASTLY over-estimating the amount of attention that the average driver pays to his or her car. Case in point, I borrowed a buddy's car a while back when my Volvo was laid up from damage caused by a mouse (mouse nest + exhaust manifold = minor engine fire + swearing). On any transition from acceleration to deceleration (or vice versa) and sometimes randomly mid-corner, the steering would "jump" 5-10 degrees causing the car to jump to the right or left. Extremely obvious and very frightening. When I told my friend about it, they said they'd never noticed it. They further claimed not to notice it when they drove the car later on. I badgered them into having a shop at least look at the car and it turned out that one of the mounting bolts for the passenger side front suspension had fallen out, allowing the entire strut assembly to shift depending on how it was loading up. (To be clear, this was not a "beater" car that I borrowed; this was a white-collar professional's everyday car owned by a person who swore up and down that they took good care of their things.)
If the average driver can't even tell when a bolt has come off their suspension, they aren't going to notice a live axle.
Bottom line: No-one's arguing that a live axle is "better." But it's an absolute fantasy to think that the average driver has enough wherewithal to notice the difference in everyday street driving. Even enthusiasts who will, however infrequently, notice the difference aren't going to (or, at least, oughtn't) be pushing hard enough on public roadways for the difference to be material. Compromises have to be made and the IRS crowd seems to completely ignore the fact that something has to give if you want to be able to buy a 420-horsepower car for $30,000.
ZV
ZV; We have had numerous heated discussions in the past few years, most of which involved throck, where the same 4-5 members flat out insisted that there is NO technical improvement with IRS whatsoever, and that ford had 'worked out' every single problem with SRA. I don't have the time to find it at the moment, but I specifically remember one thread where throck was literally the only person saying IRS is technically superior, and at least 4 members had lengthy posts on how Ford spent enough time and money to work out EVERY technical deficiency of a SRA. Those types of discussions are what prompted this thread.
Now we have some of the same people finally admitting that yes there's a difference, but it is unnoticeable (false). We have others (such as yourself) who have fully conceded that there's a difference, and it is noticeable, but now it's only to enthusiast drivers pushing the limits of their car on the street.
I have not owned a mustang specifically, but I have had quite a few tuned SRA performance vehicles and I've put at least 500++ miles on a mustang GT (~'10) in the mountains and have been a passenger for another 1000 or so.
It is absolutely false that these differences are rarely noticeable. You do not have to be driving at 9/10ths or even 5/10ths to see them come up. You do not have to be in the mountains or a track to feel and notice them. Hell, you don't even have to be in the car to notice it.
It's something that requires only a cambered uphill turn. You can be going 5/10ths, powering through the corner (nowhere near breaking traction or inducing TC), and merely hit a small bump to drastically upset the rear end. Will you instaflip into a ditch? Of course not. But it is extremely noticable, both by a driver and passenger, and anyone behind you if they are paying any attention at all. If you're driving at 5/10ths then no big deal, the rear end shakes for a few seconds until it finds a flat section of road. If you're (albeit stupidly) driving at 9/10ths then you just might end up in a ditch whereas IRS would've kept you on the road.
No one has said it's dangerous, and certainly every IRS supporter seems to have no problem acknowledging that SRA is there to fit a certain budget. The historical problem with the pro-SRA people is the blind defense of the technology, cost aside. We have had at least 5 mustang threads derailed by this exact conversation, and I have to say it's refreshing that the 'regulars' are at least conceding that there is a technical improvement with IRS.