There is likely a difference of experienced when it comes to whether a student is studying in a private or a public school. I had the chance of experiencing both and I would say that being in a private school actually feels better, but if you want complete challenge and to see the realities of Philippine living, you might want to try studying in a public school.
The comparison usually boils down to the population of students who enroll in each institution. Most likely, compared to a ratio of 30:60/70 [30 being the number of students from the private schools and 70 being the number of students in public schools per class], it could be assumed that the quality of education also differs.
In fairness to the teachers of both public and private, I had a great chance of working closely with them when I was in high school and I would say, both groups of educators try their best to provide the students what they need, Some public teachers even stretch their own budget to meet the needs of their students [like buying their own chalks and providing papers to their students]. However given the circumstances, it is of course easier to handle a class with 30 students than one that has 70 students packed in a small classroom that is even lacking in ventilation.
This is perhaps the reason why many of those who can afford it rather go to private schools. With public schools being "free" when it comes to tuition fee though, the enrollment rate still bubbles out every year in these institutions. Perhaps if only the government would provide higher budget for public schools, the situation of public high schools in here in the Philippines would improve radically.