Under 50 yards I would take the 20 ga, BUT!!! as with anything else a person should have the "Right tools" for the job. and if I wanted my son to get his first deer I would make sure he had the right tools to do it. To me (and this is just my opinion) a person hunting deer with a smooth bore shotgun is just wasting their time, You never know where they are going to hit, and that is just a fact!!! for under $200.00 a person can pick up an H&R tracker II with a rifled barrel, granted it is a single shot but hay!!! Learn to shoot. I for one think smooth bore shotguns should not be allow for deer, nor a 222, I know they will do the job if proper shot placement is used, But for the most part, anyone using a smooth bore shot gun doesn't know much about shot placement, and as to the 222 there are just better calibers, JMOP Doc
These can be had for well under 2 bills in 20 or 12, no reason to use a smooth bore