As the Tolley boys were proponents of choke-boring, we might get a better glimpse of what this particuar 4-bore SxS was intended for via an examination of the bores up to and at the muzzles.
Typically, when we see choke-bored tubes, we see the 'not for ball' note or proof stamp, from all around the world too.

My bore rifles are both 16b light SxS rifles, almost certianly meant for light-skinned and/or smaller sized game -- definitely not for big dangerous game use. They both have flip sights and they both have fully rifled bores, both of them shoot roundball quite well.

Click on my avitar photo, you should be able to get it to upsize pretty easily. The pair of holes down on the lower left corner of that target are it's first breaths in likely over a hundred years, shot at fifty yards.
The rifling doesn't seem to do any harm!

--Tinker