I cannot vouch for other people's experiences, and I'm not going to touch upon the many different meanings of the number 432 as per the subject of this thread, but when it comes to a musical instrument tuning where the middle A on the piano — which is the reference point for all other instruments in the band or orchestra — equals 432 Hz, then I personally feel that there may be a lot of suggestibility at play on account of the benefits of "A equals 432 Hz".
The thing is that "the middle A of the piano keyboard should equal 432 Hz" doesn't have any natural reference point whatsoever, because the Hertz as a unit of frequency represents the number of full sine vibrations per second, while the second as a unit of time is an entirely man-made construct — and not even an accurate one at that, which is why we have leap seconds. Furthermore, the speed at which Earth rotates around its own vertical axis — which is what our 24-hour clock is based upon — isn't even constant. Earth is actually slowing down in its rotation. During the time of the dinosaurs, an Earth day lasted only 21 hours according the standardized length of an Earth hour as we know it today.
What I will however acknowledge is that the tuning of stringed instruments to have the A note equaling 432 Hz may indeed relieve certain tuning stability problems and may possibly feel a bit more pleasant, even if only because tuning everything down to a slightly lower frequency also puts less tension on the strings, and — something which might easily be overlooked — less tension on the strings also means that the strings will be closer to the frets, because there is less string pull on the neck of the instrument, and thus there is less neck relief (i.e. less upward curvature of the fingerboard from the neck heel toward the nut). So the strings of a guitar, bass guitar, banjo, mandolin, et al, will be easier to press against the frets when the A is tuned to 432 Hz than when it is tuned to 440 Hz. But then again, a lighter gauge of strings could result in the same additional comfort without dropping the A to 432 Hz.
Being a guitarist myself, I can't say that I have ever heard or experienced any difference in quality, other than the slightly reduced tension on the strings when the guitar is tuned below concert pitch — i.e. which is where the middle A on the piano is tuned to 440 Hz. Concert pitch works just fine for me.
I do use different gauges of strings depending on the guitars I play. My Gibson guitars have a 24.75" scale length, and there I use .010-.046 strings — my Gibson Les Paul currently has .010-.052 on it, but I don't like the sound of that, so I'm going to go back to .010-.046. My other guitars have a 25.5" scale length, and on those, I use .009-.042 strings. In spite of the slightly longer scale length, the .009-.042 gauge has less tension on a 25.5" scale neck than .010-.046 on a 24.75" scale neck.
And it's not so much the feel of this tension on my fretting hand that matters in this context, but rather the feel of the tension for the picking hand. My Gibsons also have a wider string spacing than my other guitars, and their necks are slightly tilted back with regard to the body due to the higher bridge construction. So for me, a 25.5" scale works best, and on a so-called superstrat guitar — so named because they are somewhat more modern takes on the recipe of the Fender Stratocaster — with the narrower string spacing, .009-.042 strings and a neck that sits perfectly parallel with the body of the guitar. And of course, superstrats commonly also feature a whammy bar, which has become an integral part of my style.
Maybe it's because I had already been playing guitars like that for 23 years before I bought my first Gibson, or maybe it's because although Gibsons are really great guitars for what they offer, at the same time, they're also quite limited in versatility — at least, they are to me. You don't even have to think about playing something by Eddie Van Halen on a Gibson Les Paul, SG or Firebird. It just won't work. But you can certainly play Santana stuff, or Boston stuff, or even the old Les Paul & Mary Ford stuff on a Strat-style guitar. It'll just sound a bit different, but a lot of that depends on the wood type and the pickups.
Many superstrats have bodies made from mahogany, which is the preferred wood used by Gibson, and just as many of those superstrats also have humbucking pickups in at least the bridge position, and in that case, commonly in the neck position as well. The real Fender Stratocaster has a body of either ash or alder, which sounds quite a bit brighter than mahogany, and in its default configuration it also has three single-coil pickups, connected to a five-way selector switch — or a three-way switch on Strats made before 1975.
Anyway, my bottom line is that it's all very subjective, and that there may also be suggestibility involved, as I already wrote higher up in this post.