Is it better to let a child to attend good private schools all t

I have two kids. The elder daughter attends the top public school in the state. The younger son just finished kindergarten in the top private school. I enrolled him both in private and public 1st grade. I am hesitating on letting him go to the public school for 1st grade or continuing all his elementary education in private. I was told it's difficult to get in the higher grade in this public school in the future because right now it's overloaded. But my son got the 1st grade spot this time.

I can see the private school has better education quality than even the top public elementary school.

Thank you very much.