gg - I don't want to start a slag off German education thread... I met a couple here who are German, lived in London and seem very happy here with their situation. They send their ds to a state bilingual; however they will move him to the private international outside of Berlin for secondary next year. It's too far away from us so I never visited it and haven't considered it.
I think the problem is for me after the bullying episodes and the total disinterst of the school and their lack of any significant response to it which characterised dd's year 1 here, I am not going to send her to another German faith or otherwise standard school.
I expect the German privates to have the same approach to teaching which I also disliked because it was too alien for me - the copying down texts, dictation, the way maths is taught, the way the class is organised, the fact that teachers lose it and scream and so on and so on. No art, no fun activities, no project work, group work etc. You may take those things more in your stride or not have such a problem with them.
I might be more comfortable with the secondary schools here but I want a totally different approach to primary. The internationals are all not ideal, here at least.
There are some English private schools starting up but I don't like the compulsory long school day (8-4pm), they don't have proper school buildings or anything either - not the equivalent of a British independent school.
Any German specialist schools (music, art, bilingual) are all 8-4. In fact here in Berlin they are hoping to make most schools compulsory Ganztagsschulen.
Situation might be very different in other parts of Germany, dunno where you're considering moving to.