I'm pretty sure I commented on a similar question some time ago but can't find anything in the archive. My case is slightly different: I too was born ans brought up in Germany, my mother is English, my father German. My mother additionally became a German citizen when she married, so she has two passports, but that is probably less relevant. My siblings and I originally were German, but have each held two passports since the late 1970s, when some form of legislation was passed that allowed us to additionally take on the British nationality. Your children apparently have both if they have two birth certificates. I never had to decide, and still have both passports, each last renewed on occasion of my name-change after marrying (a German). AFAIK the problem of having to decide exists in families descending from immigrants, mostly from Turkey, who have taken on the German nationality but not given up their old one, whereas your children descend from a German (and were born here), so they have a stronger "right to be German", as it were (sorry, I didn't know how to put it better). But if you're not sure, your best bet would probably be to ask at the British consulate, if you live in Germany, or the "Einwohnermeldeamt", stressing the fact that the Father is German etc.
And please post the reaction here, if you do so - I'd like to know if I've been an illegal alien for the last twenty-odd years!!