It all comes down to personal preference and what you can afford. The children attend public schools in Amsterdam and they are studying, so public schools are good for kids. Public schools are often very diverse and mostly draw students from the local community. You can also choose the best elementary school in Amsterdam for your kids.
If you go alone, note that some are faith-based and follow religious programs with very ancient values, often just girls and boys. They are proud of this sport and many of them run an excellent training program. They are usually well funded, which is to be expected as they also receive government funding from public schools.
Not everyone can afford to send their children to the best private schools, but don't despair, some public schools regularly beat the best private schools on the school table despite poor funding.
You need to remember that even public schools are not completely free, and the best public schools in grade 12 can charge up to $2,000 per year per student. You can say voluntary contributions, but if your child has to participate fully, you will be asked to pay, so you need to budget for that.
Expenses are one of the factors that determine where we send our children to school, the other is where we live. Most parents need to live close to where they work, so it often depends on which school is available to you. Remember that quality education is not just results.
The best way to judge the quality of a school's education is not by the end result, but by the difference it makes, taking into account the student's starting point. large differences in the "value added" of students' performance levels and life chances can lead to a better education, even if the score is lower than 12 years. So to see things, not just results.