It depends on how accuracy is defined,Trig.
I can keep my rifled choke tube,peep sighted 870 on a 6 inch spot at 50 yards under field conditions, 2 1/2-3" from a benchreat.So on a stationary deer, I could take a 100 yard shot with a good expectation of a good hit and short bloodtrail.Trouble is,concern for a humane,swift death means getting closer than that.
But there's lots of variants. Expertise, conditions, adrenaline, and the potential accuracy of the weapon and ammo are some of the factors.
Rifled bbls,everything else being equal, tend to be more accurate with proper ammo, usually the sabot loads. Downside,deer leave longer blood trails than with the Forster type slugs or the Brennekes.
Smoothbores tend to be less accurate, but accurate enough at realistic hunting ranges in the East.
Maybe 15 or 20 of the deer I've taken have fallen to slugs. The farthest was perhaps 60 yards away.
There's lots of old threads about this, IMO a little research can answer your queries.