It is a pretty big difference. We have a 40-50 mile ride we do every year. I make the kids start off the season riding the stock fat, soft knobbies. We did 20 miles this weekend. I will be swapping the tires out this evening for their 1.2", 90psi slicks this evening.
When your son gets to a 20" wheel bike, look for tires classified for recumbents. The distributors group the tires such that if you tell your shop you want a 20" tire for your kids bike they won't find very many narrow, hi-pressure, slicks if at all because they won't be listed in the kids section. Tell them to check under recumbents for some better choices. 1" might be a too narrow for most kids rims so I err on the safe side and get 1.2-1.5, 80psi or higher, minimal tread. They will cost you ~$20/tire but are very much worth it if you plan to do longer rides.