You won't give up much to a modern shotgun other than time required to reload. I use an old Dixie Arms 10 ga. double for birds, works just fine in the rain when I'm grouse hunting. A single barrel is much safer to reload. With a double gun you better pull the unfired cap, as you will be working over the muzzle. Also suggest placing the ram-rod in the unfired barrel as you are recharging the fired barrel so you don't end up with a doubled load in one barrel, done that once. Teaches you to NOT get distracted! I occasionally shoot Sporting Clays, and do as well with the muzzle-loader as I do with a modern shotgun.
A patched round ball in the smooth bore works a little better than an unpatched ball, but without sights making a clean shot beyond 25 yds is pretty iffy.
If you are building your own, get two barrels,one smooth and one rifled then switch them as needed for whatever you are hunting that particular day. I have a Kodiak .72 cal double rifle and a 10 ga double shotgun, the barrels and stocks all interchange. I have a .62 rifle/ 20 bore with a very slow twist (1:144"), and it does double duty as a rifle or a shotgun with 20 ga AA wads and an overshot wad.
Bp puts the "hunt" back in huntng, go have a bunch of fun.