The 12's definitely kick more than the 20's. The 12 does have a range advantage so if you need to have 40 yards or more get a 12. If you don't mind settling on a max range of 30-35 yards get a 20, your shoulder will thank you for it. I personally settled for a mod choked 16, with standard game loads it's good out to 30 yards. I killed a bird with it a year ago at 27 yards and it worked fine.
These shotguns are perfect carrying in the woods all day so either one will treat you well.