You'll get plastic residue from both, to at least some degree.
In a normal rifle barrel, some form of metal (copper jacket or lead bullet) will contact the rifling and eventually reduce metal-residue/trace fouling in a new barrel as friction wears and polishes the usually relatively sharp lands.
New rifling is more prone to accumulate trace metals, older rifling less so.
In a rifled shotgun barrel, although there are still many who use lead slugs, probably the majority of shooters nowdays are using sabots. Sabots are a "conventional" bullet encased in a plastic drop-away sleeve. The jacketing on those bullets never contacts the rifling, it's always the plastic, and plastic has a far lower ability to polish out the rough spots on the rifling.
The sabot will leave a plastic buildup in the rifling, so will the plastic shot wad or cup in a shotshell.
Neither will polish the rifling like a normal bullet would, or even a steady diet of soft Foster-style lead slugs or harder Brennecke slugs. You have to watch for plastic buildup in the rifling with either sabots or shotshells and clean accordingly.
This is not saying you have to scrub the bore after every shot with a sabot or a shotshell, or after every ten shots, or after every 50 shots. Your bore and your loads will vary from other guns & loads.
Plastic composition also varies between sabots (designed for rifling) and shot cups (not designed for rifling).
I even get plastic and lead buildup in my smoothbores that have to be aggressively removed. Rifling gets it too.
Short answer (I know- too late) is that both will foul the rifling at some point.
Denis