The selection of the best depends on who achieves the academic status of the professor and the level of teaching excellence and good financial support.
This relies on the socio-political situations of the country where you would decide to work. Generally speaking, working in a public university offers more protection to the staff and insures a more steady work environment.
It depends on the point of view of the scientist. If for financial purposes then I prefer to work in private universities. If for the sake of better higher education and better discipline in the country then public universities is the option. I experienced this during my day life in teaching here in Iraq.
Dear Dr. Almadhkhori really thisq nowadays is elusory question!!!, because many colleagues thoughts that private University provided very good finance income in compare with low finance income in the public University, but it provided a well protections for their academic faculty staff and the other workers, in compare with the private one.Therefore, I prefer the public University than the private.
I like both about equally well from work experience in both. For each case individuals make the difference for quality experience and lasting relationships.