I just fitted the input 12AT7's on my VTL mono's with Herbie's Hal-O dampers. At first I was skeptical, because in a preliminary 'unplugged' test where I just tapped the tubes when pinched lightly at the pins and tip between my thumb and forefinger and listened to the airborne ring of the glass envelope, the dampers really only seemed to slightly modify the pitch and duration (as Hee suggested above), but they still rang nonetheless. Not only that, but the actual damping pads are quite bouncy when dropped onto a hard surface, which to me is more the characteristic of a spring than of a damper.
However, when I compare with the Hal-O's both on and off the tubes installed in the amps playing music, there is a (mostly) worthwhile difference to be heard through the speakers. Specifically, the dampers can help in taming brightness that is likely spurious, the result of resonances. I suspect that the Hal-O's can't help much with tubes which are themselves significantly microphonic. The benefit I heard was with tubes displaying no audible microphonics at normal volumes through the speakers (not headphones) during the tap test. (BTW, the tap test is perfectly legit - it successfully identifies microphonic tubes. What else does anyone need from a microphonics test?) I admit I was kind of suprised to hear much of anything at all with tubes that didn't seem to have any obvious problems beforehand. Just goes to show how critically sensitive all input tubes are.
A potential bit of downside can be a minor loss of 'air' - which could also be a spurious artifact itself - along with a slight diminishment of perceived 'snap' or 'jump'. On balance, in my system, the tonal balance correction is more significant. I don't want to get carried away though - the total effect is small, but consistent and to my overall liking.
I doubt there's anything special about the Herbie's dampers' sound in relation to the all-silicon ring-type dampers ; in fact, the Hal-O design, which creates an added partially-damped suspended mass to resonate, in the form of the Teflon 3/4 ring, might not be as ideal as something that contacts the glass all around and is lighter in weight. But the Hal-O's seemed like an appealing design as far as being easy to install and remove even when the tube is hot, are just as cheap, and they can look kind of cool. Since I haven't yet tried any but the Hal-O's, this is just speculation for now.
I've also got no experience with dampers that take the opposite approach and go for high mass, usually through the liberal deployment of brass. To me, these seem like they would unavoidably retain more heat, wearing the tubes out faster, and given what they cost, I don't know if I'll ever try any out. The Ensemble Tubesox look interesting - and like they might give the best damping of anything - but are also expensive. Again, it seems to me they must somewhat increase heat retention - something the Herbie's design avoids completely. I've used the Pearl tube coolers on several tube types, both output and small-signal, for a number of years, and though I think they perform well in their intended job, I can't say they do much to quell microphonics, and can even ring a bit themselves. (It also seems as if they would provide a more efficient means of picking up airborne vibrations ; in the VTL's, I use them on the hotter-running driver tubes, but not on the more vibration-critical inputs.)