Which is better, Beijing International School?

Well, yes, the two schools you mentioned are not bad. They only recruit foreign students or hold green cards. Before applying to these schools, at least one parent has a foreign permanent residence permit. I recommend several good international schools for your reference.

Shunyi international school

Beijing Jingxi International School

Beijing Dewei International School

Beijing British International School

Beijing Yaozhong International School

If you choose an international school, you'd better choose a pure international school. I hope you are satisfied with my answer.