I've tried almost all pads mentioned here (I think all with the exception of the black Roo pads, though I've tried Roo pads, both black and white, for saxophones). "Tried" means anything from testing them (installing a few and checking) to full overhauls.
Re the issue of non-stepped pads (mentioned by Gordon), it's not very common, but it pops up occasionally. It could be anything from the non-stepped pad not even covering the tone hole, to just barely closing less firmly on the edge. In the latter case it might sometimes become an issue that the pad starts to leak earlier. In the former you can't use a non-stepped pad anyway, which is pretty rare, but I did see it recently on a pro model oboe.
Re the synthetic leather pads by Music Center (also mentioned by Gordon), they are excellent, basically anything a leather pad is but better. I'm not sure they even make them for clarinets, but either way they are only special order, not even listed on their website anymore.
For synthetic pads, I've used Valentino Masters and Greenbacks, Omnipads (both firmness options) and the new ones from Music Center (both plain model and with synthetic bladder). Basically I think all of these are now at a point that they are good, Valentinos have definitely improved since some years ago. I'm still not sold on them for the larger keys, in particular the F/C and E/B open keys.
Gordon is right about the foam layer, but leather and bladder also are not completely smooth to a certain degree. The question is what degree that is and how it affects their seal. IME there isn't a significant difference in that regard, but I think the foam being slightly more springy does have an affect (a quality that is generally bad for pads). However not enough to make a difference for smaller pads and for now I actually recommend (and use) synthetic pads for smaller keys (not using animal products being another advantage for me).
Cork pads are very good, but I don't like them so much because of their feel and "noise". I use quotes because it's not a bad thing, I just mean the sound they make when they contact the tone hole. It's not that much louder, but it is the type of noise itself that I don't like. So just personal preference. I actually don't like too quiet pads and prefer to have some "noise".
Leather pads are also very good. They tend to be or feel a little softer than bladder pads but it really depends on the model. Sometimes it's the felt, but sometimes they use the same felt, so it's the leather layer itself being a little softer. They tend to last longer than bladder pads but assuming both are good quality, both types would last a long time, with some exceptions.
Re pads making an instrument brighter, darker, etc. the different feel and "noise" of different pads can make a significant difference to how they seem to sound.
For example re what bandmommy mentioned, a Selmer Signature (and Recital for that matter) is a pretty unique model and would have feel and sound different to an Evette Master Model even if they had the same pads.
Re Goretex pads, they are common on some models, like buffet pro models, maybe Selmer, Rossi, and maybe a few others. They are basically the same as bladder pads but have a layer of teflon over them. They are absurdly expensive. Their only advantage is being stepped and lasting longer than bladder in that the sealing layer is less likely to tear. If tearing is not the issue, IME it's at best as good as bladder. I don't think they are worth their price.
