What kind of accuracy and what kind of distances are we talking about? In almost every case a rifled barrel will be more accurate than a smoothbore. However I want to make sure you don't have unrealistic goals in the first place.

How does your current gun shoot? What kind of groups are you getting and at what distances?

And if you do get a rifled barrel get a cantilever scope mount. This will let you mount the scope directly to the barrel instead of to the reciever. It is a more accurate way to mount the scope since the barrel in these guns are not fixed to the reciever. When you take the gun apart to clean it do you re-sight it in? Because you should. It is very possible for the impact point to shift when you remove the barrel and put it back on. Heck if the barrel is loose enough in the reciever it could shift from shot to shot. I highly doubt that is the case though.

As far as a 20 vrs a 12, shoot whatever you like. Obviously a 12 will have more power than a 20, but they will both kill deer just fine out to 100 yards with the proper ammo.

Keep in mind a rifled barrel will not make you a better hunter. It will just make the gun more accurate. Depending on how your gun shoots though it could double your effective range.

Paul