Hi Dave!
I had the same question, and learned the "Quadra" moniker referred to Thudbuster's development of the parallelogram linkage (as opposed to their earlier designs, see:
http://www.thudbuster.com/history.html ). Now, regardless of name, they all seem to be simply "Thudbusters" in one of two styles: ST (Short Travel) or LT (Long Travel).
One is not simply a cut-down version of the other. The pivot pins and bushings are essentially the same, but the links differ in length and the elastomers differ greatly. The ST uses a molded, rubbery puck that comes in a predetermined hardness (durometer). The LT uses urethane elastomers that can be stacked in various durometers to fine-tune the action of the post. Both posts offer a sort of rebound control (based entirely on the rebound characteristics of the elastomeric medium), but the LT has a "hard lockout/preload" bolt that allows adjustment of both characteristics. It's longer linkage makes for a more supple ride on larger bumps, and it is more finely tunable. The ST is a more generic suspension option and its more limited travel makes it most suitable for smoothing out road irregularities. I particularly dislike the "buzz" of chip-sealed pavement, and the ST proved to damp that out nicely; same for concrete expansion joints, but it is not so good for absorbing larger irregularities like tree roots, big potholes, and rough gravel ballast on logging roads. The LT excels in those conditions. I've found both 'posts to be quiet in normal operation. Both work nicely with my Brooks B.17 saddles and don't interfere with the Brooks rails.
For the Nomad, I thought long and hard and decided to get the 27.2mm version (same as Thorn originally specs for their rigid 'posts) so I could continue to use the original Thorn-supplied shim. Andy Blance has made a good argument for the shim, saying it makes seizure due to galvanic corrosion less likely. For me, another factor was the ability to quickly switch between rigid and both sus-posts for A-B comparisons during testing. I was skeptical as to how well a TBLT would work for my needs, so I tried the ST also. It helped, but not "enough" for the MTB-like conditions I ride, where shock was worst when unladen. Once I fitted the LT there was no looking back and it has remained in place ever since. I would have preferred the LT model even for my road bikes, but their horiziontal top tubes only have enough clearance for the ST model, which has proven to be a great improvement over rigid seatposts for my general use of those bikes. For them, I ordered the specific sizes needed (26.8 and 27.0), since I had not previously used shims on them and did not want to (the top collar of a shim would have conflicted with their concave seat lugs).
While I'm happy with both the ST and LT Thudbusters, I have a really smooth, light, high-rev pedaling style that minimizes any bobbing in the saddle. I think if I were a low-rev, high-torque "masher", the LT *could* possibly have a problem with bobbing until the rider adjusted pedaling style. It has not been a problem for me. The ST with its more damped, limited travel doesn't seem as likely to bob under a masher.
About a year after fitment, the LT developed a click while riding. After following all the suggestions in the Thudbuster FAQ, I wrote their support team and received a supportive note in reply, as well as a replacement bushing kit. It seems something was amiss in only the right-side lower bushing -- perhaps it had been slightly damaged on initial installation? -- and replacing it solved the problem completely. I have kept the others for spares, but anticipate no problems based on how well the other bushings are doing. I've had good luck lubing with Tri-Flow, and I think the neoprene covers are a very good idea to keep the bushings dry and clean.
Thudbusters are available from a number of vendors internationally. If you are shopping for one in the US, the inventor sells direct from his site (
http://www.thudbuster.com/ ), with drop shipments dispatched by Cane Creek. The other direct site is Cane Creek, who makes the posts under license (
http://www.canecreek.com/products/seatposts ). I decided to buy from the inventor 'cos he included the neoprene sleeve for free.
I was initially reluctant to go with a suspension 'post out of concerns for long-term durability, maintenance, and wear. I think that is still a potential issue, and won't know if it is an actual problem until I use the Thudbusters more. For the Nomad's LT, I will include a spare preload/limit bolt, nut and washer in my touring kit, as a breakage there could disable the post and there have been isolated, rare reports of breakage. I think the bolt could be an eventual wear item, due to the friction of the elastomers sliding on the shaft, as well as cumulative shock loads on lockout, so why not take a spare if going into the Middle of Nowhere? The ST has no such bolt.
I have found both types of elastomers (ST and LT) tend to "sag" a bit with use over time. It is not a material concern, but I found it helpful to place my saddle 5-8mm forward to compensate for sag (the linkage in the seatpost causes the saddle to decline downward and rearward under load and it proved to be a bit much when running the saddle with the same settings as on a rigid 'post). I've found saddle-to-BB distance to remain essentially constant, so it has not affected my knees adversely. I do notice compression places me the same distance but rearward in relation to the BB, but this has not been a problem in practice.
One more observation: The LT arrived with Medium elastomers and proved to be fine for my 78kg body weight, I didn't even have to adjust the preload/limit bolt. The ST was a different story (Nomad and each of the two randonneur bikes, all set up for identical position on the bikes). With my preferred 45° back angle while riding the hoods and even more shallow back angle while on the drops, I just did not have enough weight on the saddle to actuate the ST posts except when hitting large bumps, so they felt harsh. They came supplied with the Medium elastomer puck (recommended for my weight) and substituting the included Soft puck solved the problem completely; the STs are now responsive, yet don't even approach bottom-out. I have concluded body weight is important in determining which elastomer to use, but so is body positioning and actual weight on the saddle.
Aesthetically, I still think Thudbusters are ugly -- especially on road bikes with classic geometry -- but they are now functionally beautiful in my eyes, thanks to their added performance and reduced fatigue with greater comfort.
Hope this helps, Dave.
All the best,
Dan.