The recoil will be a little lighter with the .223 but muzzle blast will be a bit more. I started my kids hunting with a 21" light contour .223(AI) and it worked well with the bullets I used. They wore ear protection. If you use the .223 consider your bullets well.
.357 Max will be a little more recoil but it's still light in a carbine barrel. Muzzle blast seems noticeably less to me. Range will be a bit less with the Max if that makes a difference.
Penetration will vary with each of them depending on the bullet used. A soft 158 pushed hard by the Max at close range will likely penetrate less than a 50 tsx pushed at any speed by the .223.
Either will work. Let him shoot both in practice and see if he has a big preference one way or the other.
