I've found that it can vary quite a bit. For example, my brother has a smoothbore 870 that shot pretty decent out to 75 yards or so. But my Winchester is not nearly as accurate- I switched to a muzzleloader because I couldn't hit anything past 50 yards with it. So some, but not all smoothbores can be accurate. But you're probably going to be limited to 80 yards or so, even with an accurate one.

A rifled barrel will generally be a lot more accurate, and it will extend your range out to 120 - 150 yards if you have a scope.

You asked "what kind of slugs?"
With a smooth bore, the key is to not use Sabot Slugs, they are designed specifically for rifled barrels. Use "rifled" slugs. In my experience, the Brenneke KO's kick some serious butt from a smooth bore with rifle sights. I'm with most here, 75 yds is a reliable maximum. If your going to 100yds, be well practiced and confident in your ability.

I have a Mossberg 500 smoothbore with rifle sights. It shoots Winchester rifled slugs into a 2" group at 50 yds. I'd shoot a deer out to 75 yds, after that it's the sights and my eyes that limit my effective range.

You will see zero pattern if you shoot buckshot through a cylinder choke, which is wht my 500 barrel with rifled sights has. I tried a couple shots at a paper plate at 25 yds. One or two pellets hit the plate.

well I shoot the exact gun. 870, smooth bore short barrel but with a scope. And you would be amazed with the gun off a rest. I'm not the best shot but at 50 yrds I have a 3" group and at 100 yrd I am always inside a pie plate. And not much drop, I don't care what the box says. And oh yea, I shoot the cheapo winchester rifled slugs from walmart. $9 for a box of 15.

I agree, nothing wrong w/ a smoothy and less finicky IMO, although i did get good results from KOs and black magics in a H&R trapper w/ rifled barrel

Shot Remington Sluggers out of a shortbarreled smoothbore on a 870 for years. 100 yards no problem with hitting the boiler room everytime.

Without a scope, they are about equal for accuracy out to about 75 yards in my opinion. You can only hold so tight with those factory sights. The tightest groups I ever got were with my Winchester 1200 which had a (gee, I forget if it was 24 inch or 26" barrell). it had quite a fine bead and rear notch, allowing for a finer hold. Fifferent slugs will certainly group different. Shoot different slugs on different days, to avoid getting flinchy, to check groups. At 50 yards I can keep the slugs touching each other out of my Ithaca with standard Winchester pumpkin balls.

I grew up shooting a 870 with the smooth bore...sited it at 50 and it only has the range of 75. Anything more than that is guessing, unless it is sited for it.

My brother is shooting a Moss 500 with a rifled barrel, 100 yards 2' group.

I hope I don't step on anyones toes but Hunting is like anything else, if you are going to do it you need the right tools, and a smooth bore "slug" barrel is not the right tool!!, Heck for $200 (or less) a person can purchase a rifled barreled H&R (NEF), I just cannot Imagen getting a shot at a nice deer 40 or more yards out and be sitting with a smooth bore "slug" barrel, shooting a smooth bore you point and hope for the best, (about like throwing a rock) with a rifled barrel you aim and if you miss it's you not the gun. also in many states buck shot is not allowed, Do your self a favor get a rifled barrel, Just my opinion Den

Remington Sluggers, I shot them for years out of my 870, I now shoot a rifled 20 gauge Encore, I run SST through it. My slug-master 512 i used Sluggers as well grouped the best through that.