I have a pretty small vise compared to most on here. ~3.5 or 4" old columbian IIRC. But hey it works.
Yea, soft jaws are just that, typically in efforts to not mar the work. The softness of the jaws is usually dependent on the work piece you will be holding. I've seen anything from copper to plastic, rubber, leather, aluminum, wood, foam, tape.
I have a few sets that I milled out of an old plastic cutting board (HDPE IIRC), some have magnets epoxied to the back side, some have countersunk through holes. A few sets made out of wood blocks, actually just milled 2x4's. But my most used ones are strips of pretty hard (sorry don't know durometer of them) orange rubber that i pulled off the bottom of a floor buffer. It was the base guard to prevent scratching the walls. These are what I typically use for the delicate stuff. Ex. rile actions, even clamping stocks. Things that are finished and cannot be scratched while holding them. They are soft and sticky to really hold the work, yet will not leave any evidence that the item has been clamped.
I'm sure you will get some better advice from the vise experts on here, but just my 2¢
