There is a big difference in recoil between a semi-auto .223 Rem and a .243 Win bolt action. I wouldn't let most under-10 kids shoot the .243 Win, unless they're big/tough for their age and have had adequate shooting experience.
I've seen 10 year-olds handle one or two shots with a .243, but subsequent shots at targets created flinches that may last quite a while. One pulled his head away from the stock, just before "jerking" the trigger.
“God save us from people who mean well.”
― Vikram Seth