I would use singular: "the kids have an advantage over those in public schools". If you use plural, it has a different meaning. It means there are opportunities available to them that are not available to the public school students. In that case, I would write "the kids have advantages that are not available to those in public schools"

Correct another example He has/enjoys an unfair advantage over us because of his wealth

Yes, that sentence could have been written by a native speaker.