Fast transients and snappy transients are different in my experience. Fast transients tend to be more emphasized with thinner earpads, due to sound of the driver needing less time to arrive to your ears, making everything sound more dynamic and quicker; you could say it’s a natural kind of snappy. It sounds smooth, quicker and natural.
I’ve found that, atleast with dynamic drivers, that no matter what the material is, if the 2 earpads are as thin as each other, they’ll have the same smooth transient response. The only differences are in texture of the treble (more sizzly with velour pads and smoother with leather) and fr response changes (more lower-mids and bass, less uppermids and treble with leather/pleather/sheepskin)
Snappy transients due to thicker pads, actually slow down the transient response, making sounds in especially the upper mid region more rough in impact. Some people perceive this as a faster transient response, but it’s just more resonance. Same with people perceiving a bright treble response as more detailed vs actual details.