They both do similar things yes. I also own a slug gun and a muzzleloader. Here in NY there is a period of time where you can use a bow or a ML for early season (northern zone) then after the main firearms season there is another bow/ML season for the last two weeks (southern zone).
On the question of the 20 gauge or 12 gauge barrel. I would go with the 20. I own a H&R Slug hunter and love it. The recoil is easy and it shoots to 125-150 or so. I don't know that I would want to shoot much past those distances with a slug gun. Give me my rifle after 150 thank you.