the gel pad stuff was on my specialized allez sport 08. the stuff is comfortable & it wont make the bars look fat tho u may want to check that out yourself. dont know about vibration dampening its just a bit more comfortable holding onto the handlebars.
I've had bar phat on my road bike since I built it 3 years ago. Don't know what the thickness is since there were no options at the time. It does lead to fairly thick bars, but I like it a lot and it gives good support. Combined with good gloves, it makes riding my road bike much more comfortable - I came from riding hybrids and riding most bikes (low position and thin tape) was unforgiving.
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Thick(ish) bars, which doesn't bother me in the slightest, but very comfortable.