The 20 ga is basically a modern inline magnum muzzle loader that you don't have to handload from the front of the barrel

. It uses the same .44/.45 cal bullets at the same weights with the same twist rates and velocities as many of the inlines do. But it does it with smokeless powder and preloaded cartridges. So it would stand they would have close to the same accuracy and down range performance as the magnum inlines do, which is quite good in my opinion. If you wanted to shoot a lighter faster bullet the 20 ga will probably give you better luck in that department.
Also from what I have been reading they seem to be less picky about what ammo they like and shoot accurately.
My 12 ga slug gun is easier to shoot and clean, but my inline is deffinately more accurate at longer ranges, and easier to find a load that works well. It's just a pain to load and clean.
They are also lighter than the 12 ga since the barrel is not as big. I don't know about recoil, I have not shot both. I bet it would really depend on what ammo you shot out of it. I am sure some of the more potent stuff smacks you pretty hard.
The 20 ga is also more versatile. The heavy barrel 20 ga is a 12 ga blank bored to 20 ga and rifled. So it sits on the 12/20 ga shotgun reciever. So if you wanted you could swap a 12 or 20 ga shot barrel onto it if you wanted. The 12 ga heavy barrel is a 10 ga barrel bored to 12 ga (this is how they get the thicker bull barrels) so it sits on a 10 ga reciever. This means the only other barrels you can use are 10 ga shot barrels.
Your best bet would be to get a Handi Rifle in a centerfire and order a 20 ga bull barrel with it. These use a receiver that will let you use most centerfires, 20 and 12 ga shot barrels, the 20 ga rifled slug barrel and I believe a 50 cal muzzle loader barrel. MUCH more versatile down the road if you only wanted one gun with different barrels. The barrels need to be fitted by H&R or a gunsmith though. You can't just swap them out like a Contender or something. Once they are fitted though you can just change them at will. All you need is a large phillips screwdriver.
The 12 ga slug guns are heavier and have slower twist rates and use 50 cal saboted bullets in weights around 400 grns. Most have reported thier guns do not like the faster lighter bullets. Some do, but most I have talked to in person and on the net don't have very good luck with them. I probably will not waste the money on the SST's because I am almost sure my gun will not shoot them well. Mine tends to like bullet weights around 1 oz (435 grns) and between 1500 and 1700 fps.
And you can shoot a rifled slug through a rifled barrel. It will not hurt anything and some are pretty darn accurate for the price compared to 10-20 bucks for a box of 5 premium sabot rounds. The down side is they make one heck of a mess in the barrel. I can get around 4 shots out of mine before the barrel fouls out and needs to be cleaned (simalar to my Inline actually

). And you really need to clean them when you are done. And it will be messy! No harm though if you clean them good, lead is softer than the hardened steel barrels are. I actually chuck my cleaning rod with a brass brush in a cordless drill and scrub my barrel that way a few times.
Paul