I agree with the other guys. Even though the 20 is really an inferior gauge based on shot collum length and bore diameter it is still pretty effective. And the ammo is cheaper and easier to find. The 16 is a great upland gauge but ammo is sometimes not readily available except at a premium price.
You never said how big you son is? If he is big enough, why not buy a full sized 870 express 12 ga. and cut down the stock if you need to (or have a gunsmith do it). He can shoot light loads with it and still be able to shoot 3" turkey and steel waterfowl loads come season. He won't feel the recoil shooting at game.
You can alway buy a replacement composite stock later on when he grows a little bigger.