Only you can answer that question but as an old person do you think you're more likely to regret your choice of school or not having a 4th child?
I've never read anything to make me believe that private schools are inherantly better than public although in some towns they may be the better option, just as in some towns the public may be a better option, so for me it's a no-brainer but I do see that if you believe private is better than public or you live in a twon with an awful public school it could be a conundrum.