Which school is better Private or Public School?

Most importantly, you will have to reevaluate your standard definition of public and private.

In most western countries, public schools are run by state funding and afford a quality education at reasonable cost.  Private schools in those countries are for the elite and rich people and more for alumni/networking/status vs. any significant short comings in the public system.  That is, you can get a good education in public schools for close to free but if you want an edge in life, you go to a private school.

In the UAE, it is opposite.  Public schools are free for locals and cost a fee for expats. In addition, the language of instruction is Arabic and curriculum is UAE national approved one.  So practically speaking, the system is not easy for expats and considering that most expats are here for a relatively temporary stay, when you move back, its not easy to move to a different curriculum.   On top, the quality of education can't be compared to, say public schools in the west, as the ones here are run by a Government bureaucracy vs. professional educators having relative autonomy, in the west.

For these reasons and others, the overwhelming majority of expats put their kids in private schools or at the very least, in schools run by their respective countries e.g. Indian school etc.