In the KSA, public school is only offered to Saudi children. From what I understand, the education is based on the Koran, and, I believe that the schools are single-sex schools. School is not compulsory. One statistic I read claimed only 60% of children actually attend school. It could be true, given that Saudi children seem to stay up all hours of the night with their parents.
So for an ex-pat family, private schools or homeschooling are the only two options. There are a number of private schools, often based on nationality, though the schools generally don't preclude students based on nationality, rather that school is taught in the national language and follows a national curriculum.
The school my children attend uses English as the language of instruction, though Arabic, French, and Spanish are all taught. It is truly international, with a wide variety of nationalities represented. Arabic children are welcome to attend this particular school, as long as they can meet the requirements--requisite schooling, passing the assessment test, and payment of tuition.
I didn't realize this until I lived in Sweden, but there is an International School system organization which accredits different schools across the world. These schools have to meet certain criteria and it is a big deal to acheive it. Both of the international schools my children attended in Sweden were in the process of becoming certified by this organization.
I think private international schools are a fine alternative for education when the you are staying in a country for a limited period of time, where public schools are not a good option, or when there are particular language challenges. Sure, my kids don't has as much foreign language exposure by attending a public school, but they certainly get an international experience that is unparalleled.
For me, it was an amazing experience to be surrounded by intelligent, educated, and engaged parents of all nationalities. We especially appreciated getting to know Muslim families. My children have grown up with children from all races and nationalities. They've come to see that there are good people everywhere, regardless of one's location.
One time, while in Sweden, my boys came home from the playground, bristling with indignation. Their neighbor, a darling girl from Sri Lanka, was being teased and insulted by another boy on the playground. His insults were of the racial slur variety. My boys quickly defended their friend and said to me, "you should always be nice to people--it doesn't matter what their skin color is."
That, to me, was the most powerful thing that came out of their international school experience. My kids didn't just say that because I had talked to them, their experience with people from all over the world really taught them that skin color, ethnic identity, or language differences are surface. People are people. They learned to enjoy differences, rather than shun them.