Does attaining a degree in a private school mean better salaries? Is there enough data to say otherwise?
When I interview people about their paper qualifications, I will watch if they are overly fixated on that. If they are, I know they are good students and probably poor workers on the real stage.
Generally, the public sector doesn't recognise private degrees. Unless one plans to work in the private sector, it is better to give up the idea of doing private degrees.
Take a private degree only if you are able to put in the effort and do well. Then, follow up with a master's at a reputable overseas institution.