in my opinion, I think private universities receive a lot of aids from their Alma Maters, NGO's etc. This aid help in diverse ways to slash part of their tuition with which the public university do not enjoy apart from the state's subsidies.
it depends on the government laws and in national department of education. The "aids" thing can hit any schools weather it was private nor public nor it depends on the status or type of school, it always depends on the school policies and security maintenance, so in making a canvass on where to study high school/ college always be sure to ask the views and opinions of the experienced professionals. Naturally facilities , quality of education and teacher's way of teaching to students in private------ school well i cannot say they are "better" however i can say that privates are much more accountable and answerable, based from personal experience. Now talking about tuition fees, public schools are cheaper simply because it is for "PUBLIC" use and there's a government policy about that either for public schools, to make sure that the public or average/ below average people in terms of financial support can afford it and not all countries have same laws and policies regarding that so do a research about that about your own government laws on your country