First: Most side by side shotguns were never designed to shoot round ball accurately, much less to the same point of aim.(POA) You might get one of the two barrels to shoot a round ball load fairly well out to 50 yds or so, but that is about it. For a shotgun to shoot both RB and shot loads will is almost in the rank of freak accidents. I am sure its been done, but it would take a lot of work to get the two different things to shoot to the same POA.
The 10 gauge is .775" in diameter. It means that 10 round balls that bore size weigh a pound. I don't know many people who shoot 10 gauge round balls, if any. I have never seen them for sale.
The 12 gauge is .729" in diameter. balls weigh 1 1/3 oz. Actually, the balls need to be smaller, and therefore weigh less , but you get the idea. The 12 gauge is a good bird gun, but do not expect to take a lot of shot past 35 yards, even if you buy a gun with the screw in, interchangeable choke tubes. The chokes help, but for good patterns velocities have to be kept down. To compensate, use larger shot sizes than you would with a modern shotgun shooting shells. One of the main differences is that most BP shotgun shooters don't want to use plastic shot cups. The cups do protect the shot from being rubbed flat by the inside of the barrel when fired. That is why they have tightened up many traditional groups in modern shell casings fired out of choked barrels.
Its now rare to find a BP shotgun chambered for the 16 gauge, and as far as I know, the Pedersoli is not offered in that bore size.
The 20 gauge is the last gauge that gun is offered in, which is .615" in diameter, or 62 caliber.
If your dream is to own one long gun that has one barreled rifled, and another smoothbore so that you can use it both for bird shooting, and then to take big game, I am afraid that you will have to look to a custom made firearm, these days. There was an over/under gun offered many years ago that came in various combinations of rifle and shotgun, but while advertised, I don't think I have actually seen that gun, other than pictures.
I suggest you consider getting a single barrel fowler, in 20 or 12 gauge for your shotgun needs. The single barrel gun can be jug choked, or I suppose that you could have it made for screw in choke tubes. Most all fowlers are flintlocks, but they can also be made as percussion guns. The, for rifle hunting purposes, buy a rifle in .50 or .54 caliber, depending on what you intend to hunt. There are excellent half stock rifles in these calibers, including guns made by Thompson/Center, Lyman, and imports sold by cabelas, and other importers. Dixie has its own lines. The prices are very reasonable considering what you get. We hear lots of nice things about the Lyman Great plains Rifle, for instance. Single barrel shotguns, in percussion can be had fairly reasonably, and there are even some imports to look at. Check out the suppliers in the Member Resources section of the index here.