If a 223 is used the bullet placement is more critical, I think. A lung shot with a 35 caliber will drop the deer faster and leave a better blood trail than the 22 caliber again my opinion.
But I'd get the kid shooting, a lot. See if he can hit a softball target and at what range. Don't let him shoot past that maximum range. Teach him the correct bullet placement. If group size isn't much different with the 35, pick that one. But I'm betting the kid will shoot the 22 caliber better.
The other thing is distance. The 35 will have a more rainbow trajectory and tougher for the kid to hit if distance is a factor.
