Private universities as gap-fillers

I just returned from Israel, where I had taught a course on corporate governance at a private university. Reflecting on my time at other private universities, I was wondering why some private universities have laxer and others have higher admission and examination standards than public universities.

The best starting point may be that private universities typically charge higher fees than public ones (though there are exceptions; e.g., private universities mainly funded by altruistic donors). Why are students willing to pay higher fees? Private universities themselves may usually say that they provide a 'better product', such as more student-oriented teaching, better infrastructure etc. To some extent this may be the case. However, this is not the entire story, given the fact that many academics (which includes me) teach at private and public universities - and, usually, they would do it in a similar way.

So, there has to be a second reason. Here, we get to the distinction between different types of private universities. In some countries public universities have relatively tough admission and examination standards. Thus, private universities fill the gap for applicants who fall below these standards. In other countries, however, public universities accept almost everyone. Here, private universities typically have tougher standards; thus, they deliberately target students who benefit from the university's elite branding and are therefore willing to pay higher fees. Finally, there are mixtures: some private universities use different strategies for different programmes; e.g. the undergraduate programme may be offered in a restricted domestic setting but not the postgraduate one [PS: I could provide examples for each of these categories but it may be better not to do so].