I have friends teaching in international schools. They hardly have anything good to say about international schools.

Private school:

Benefits
- Your kid can gain connections to other richer kids (think of Jho Low)
- Nurture your kid to speak up
- You get what you want (It goes to the first point under Cons which will make your kid lazy)

Cons
- It's all about spoonfeeding in international schools. May not be a good learning environment in the long term. All of my friends consistently complained about this. Need to spoonfeed the kids all the time to avoid complaints from parents. Well, it just make the students lazier.
- Lack of discipline
- Expensive

At least in Chinese schools, they still enforce discipline among the students. Anyway, there are still gang and disciplinary issues in both chinese schools and international schools. But at least, the students are more disciplined in chinese schools.

Chinese schools

Benefits
- Better discipline
- Get to learn mandarin

Cons
- More homework
- May stifle creativity and the students tend not to speak up

The choice is yours