We moved when DS was nearly 5 and he has integrated fine in terms of language. He did 2 years of kindergarten, which in hindsight was too many, he would have been fine at school after one but the assessment they do wouldn't have passed him with his lower language level 6 months before the starting date.
9 and 11 might be tricky in terms of school selection because at 10 most German kids move to secondary school and they are all streamed in some kind of incomprehensible system which is massively stressful/confusing to foreigners. DS is 9 so we have this all to research just after Christmas.
However school woes aside it genuinely is lovely and brilliant here for kids, I am so glad he has the kind of lifestyle/freedom that German kids have, it's wonderful. The summer holiday activities are all fantastic as well - there's so much choice! We're also doing assessment at the moment for ADHD for him and I can't fault it - it's been really simple and supportive whereas friends back in the UK have had an awful time with waiting lists and generally having to wait until the DC show really serious issues before they can get anywhere with it. I've also had excellent experiences with the healthcare here in general. DH and I both had quite serious accidents last year which have been dealt with well and I'm expecting DC2 now and I've been impressed with the care I've had regarding that as well. Everyone has always made us feel as though they had infinite time for us - quite the opposite of harrassed/rushed NHS staff :(
What you need to know:
Bring your own tea and get it posted regularly because the tea here is all terrible - but the coffee is nice. Typhoo is good to import because even their massive packs are individually divided into sets of 40, whereas a 260 box of Yorkshire Tea will go stale unless you drink loads of it.
People can be quite blunt but you get used to it and I kind of appreciate the straightforwardness now even though I can get annoyed at the time.
Paperwork is horrible and the bane of your life. Just swear at it a lot and use google translate or be really nice to some German native speaking friends, offer to bake them a Victoria Sponge or something and hope they will help you. It doesn't come up that often so it's not too much of a hindrance.
Use an online software thing to file your taxes - DO NOT try to do it yourself using the official one. It's absolutely worth paying the €30 or so for the software to find all of the little loopholes, things you can claim back etc. Or use a tax advisor. But I find the software approach is the best value for money.
You need to get a form from the Jobcentre when you leave the UK confirming that you're no longer receiving child benefit. This will enable you to receive German child benefit (Kindergeld) for your DC which is a bit more generous than the UK one and they'll backdate it - but you need the paper. You might have to ask a couple of times because half of the jobcentre staff don't know that it exists.
When people post stuff to you if you have any 7s in your address, make sure they cross the 7s or print the address from a computer, otherwise your post will go completely AWOL and you might get it in a few months or never at all. Germans write their 1s like we write our 7s.