For the poor, private schools is no option. They don't even consider it.
For the rich, public schools is no option. It destroys their stature making them labelled as cheap for the coming generations. There are very few exceptions to this rule, very few.
The families struggling with it are those reamining in the middle class, who really suffer with the high expenses of educating their kids in private schools, and wonder if it's really worth it.
I'll try to point out what a private school offers that public schools do not.
1- Foreign Langauges. There are more English-class lessons in most private schools, although I know quite a few graduates from such schools who are horrible in English. I know quite a few public school graduates who used to take extra lessons for reasonable prices during the summer or were fortunate enough to have excellent English teachers in school and they really excelled in English. I still have to say that private schools helps you think in English and not just speak it.
The other langauge is French. I attended the National Orthodox School (Orthodoxiyyeh) for 11 years, took French for 9 of then, was always top of my class in French, was top of my school in the Brevet test, but was never able to fully communicate with a French-speaking person. I have to say though that had I lived in a French-speaking country right after graduation, I would have mastered the langauge much more easily than someone who never took Fench classes. More than 90% of my class knew NOTHING about the language after 9 years of studying it although we had at least 3 weekly classes in French.
Also when I was able to learn Spanish later in life much more quickly because of the similarities in French and Spanish.
I remember some graduates of other schools like Frere, the Rosary school, and Lady of Nazareth were really fluent in French. So if you're really looking for your kid to learn French there's a way to go with these schools.
2- A non-Tawjihi program. I totally sympathasize with parents who do not want their kids to sit for a Tawjihi program. I'd rather have my kids do GCE/IG or whatever British system is there than do Tawjihi. Public schools do not offer that, and it's so overwhelming for a student to sit for exams in both systems although they can independently do the GCE tests.
I sat for GCE and my school had some really outstanding teachers. Some private schools have worked hard to provide well-trained and experienced teachers and their students score very well. However there are quite a few schools who consider these British systems a way of collecting more fees from students, since students in these classes pay astronomically high fees. Many of these students are really not hard workers and they join the British system because it's "cool" and believe they don't have to work as hard as Tawjihi students. They end up learning the hard way that they were wrong, and the school does nothing to alarm them. Besides, many IG/IB teachers are just teachers who speak English and are not trained to specifically teach this British or American material to their students.
There can also be a very rich Arabic material in the British system. I studied the Jahili, Islamic, Ommayad and Abbasi potery very extensively. I mastered grammar, I was really able to "a3reb" every single text written in Arabic including poems, verses from Quran and road signs. Translation too was vital to passing these tests. So don't forget about your kids forgetting their mother language if they study in English for 2 years in high school.
3- Extra-Curricular Activities. First, remember that most private schools charge a lot for such activities like music, drama or sports. Students in public schools can join these activities in different centers in Amman for cheaper prices. Some private schools offer very little in terms of these activities. Again, look at graduates from these schools. Most graduates of private schools do not really excel in some extra-curricular activity and most of those who do (like in playing piano or singing) did so because they were trained by somewhere other than the school.
4-Learning Christianity, that's only available (as far as I know) in some private schools. I know some Christian parents who really struggle to afford fees for their children just to keep them in a private school so they can learn the religion. However some churches teach Christian classes although they're not as intensive as the ones schools offer.
5- Mixed Schools: Some people like me believe a school should be mixed. There advantages of having boys and girls study together outweigh the risk, given that they're closely watched and certain rules are strictly applied. I studied in such school and we had a very healthy environment. that is something that's available in private schools only so you may view as an advantage.
6- Transportation. Private Schools provide transportation for your kids. Again, parents have to pay for this and it's usually a lot of money, but at least they have the option.
7- Better teaching???? That's a tough one. I really don't have an answer for this. I saw some awfully horrible teachers in private schools, but the good thing is that they did not last too long. The administrators in my school usually listened to parents' complaints and may fire a teacher if s/he is not doing his/her job appropriately. That might be the case in some public schools too where the administrator is really dedicated to their job and do care about their school's reputation. Now if you go outside Amman, you can find a whole bunch of public schools where most students fail at Tawjihi, mainly because they didn't have a physics or biology teacher in 5 years, or because there were 50 students jammed in one unheated class in a 5-degree weather where there isn't a chance to ask a single question.
Having said that, you need to look at Tawjihi scores and you'll find out that a lot of top students come from public schools. It's usually the same 4 or 5 public schools though.
In conclusion, there are some potential advantages of some private schools over public schools, but you can easily find a public school that is better than many other private schools. One thing for sure, is that you're not ending your kids future with placing him in a public school. The money you spend in a some private schools is absolutely not worth it and will not pay back.