^Good tip on pad-swapping there. I don't know if anyone attempts to replace pads by stretching them out, but that's a bad idea; the "inverted edges" approach is much better.
In general, the type of pads (and for in-ears, the type of tips) are thought to affect the sound. There's good reason to think so: with speakers, the materials in a room can affect the sound you hear, because the sound has to bounce off those materials before it reaches your ears. Headphones aren't too different--the space between the driver and your ears can be thought of as a 'room', and the sound must bounce off the earpads before it gets to your eardrums.
This is why people sometimes say closed headphones sound "plastic-y", since the sound must bounce off the plastic earcups before reaching you. Not all closed headphones are as badly affected though, and in my mind, the HD 25-1 does a very good job of not sounding plastic-y.
Between the HD 25-1's two earpad types, the biggest potential difference could be in how much they isolate, which is directly related to how bassy they can sound. More isolation, more bass, yes? Having said that, I don't recall there being a huge difference in sound between the two earpads,so I stuck with the more comfortable one.