Cotton will, at least in the case of the cotton underwear I've tried v. the Buck Naked's that I've tried- feel more "soft" to the touch at first. Think fluffy bunny. I find with extended use and repeated washing this may in time turn into a texture akin to a washrag, or a cheaper towel. Sort of a rougher feel, not rough in of itself but now closer to a gritty/sandpaper feel especially when dry, than the former fluffy bunny feel they had new.

Very well could be the cotton blends I've used though.

Nylon isn't fluffy bunny, but it also isn't abrasive. It's tricky to explain but in keeping with its sister synthetics like polyester, which you may have some experience with from exercise shirts or the like- it's just sort of smooth.

I think part of the fluffy feeling for clothing comes from loose fibers that are sort of frazzled or sticking out of the main weave. Maybe similar to how the hair on your head is a bunch of individual strands sticking out which normally are a soft and fuzzy/slightly springy mass if you press on them . But if you take those hairs tie them together into a tight braid or what not- it's not the braid becomes suddenly uncomfortable... Just more dense with less give/bounce than a loose head of hair, but still smooth to the touch. That's how nylon feels, smooth but dense. Cotton starts off with that fuzzy feel, but over time drops off to a much less appealing state.

In my experience a basic cotton garment can feel rougher than synthetics especially over time, in most cases.