I really wouldn't do this. Not sure how parents can treat their children so differently. I have cousins who suffered this situation, the sons went private and the daughter state. It's still a wind up for their parents at family events etc. To be fair, the siblings are fine with it but I think that is because they have all done really well and are very happy. Not sure how they would be if it had played out differently.
As some have said, treat then the same and use the money to add to all of the childhood experiences.
It really isn't the be all and end all. Don't stress about it. We have fab state school here.