I have a 12ga. and my daughters have 20ga shotguns. All the deer they have killed are just as dead as the ones killed by my 12 ga. The 20ga they have is an 870 Youth with a rifled open sight slug barrel. Excellent choice, only modification was fiver optic sights. They are short, manuverable, and accurate. If I did not already have my 12 ga, I would have the same gun. I am 6'3", and it shoots very accurately even in my hands.
If one of them stays home when I go out rabbit hunting, I use one of their 20ga with the smooth bore barrel. When you are in thick brush, it is very maneuverable.