as long as you belong to their own Volk you have not much to fear
As long as you were not gay, handicapped, mentally disabled, suffering from mental illness, or being seen as a social nuisance (which sometimes could apply to a single women who was reported for "undue behaviour". The Nazis killled and persecuted Germans who belonged to all of those groups. Belonging to their "own" would not save you. In fact they considered it their duty to "purify" their Volk from those elements.
No offense, but you should inform yourself a bit more about what the Nazis did to other Germans. It was shockingly easy to fall through the cracks. And it was just as easy as in a communist dictatorship to be suspected of subversive behaviour.
they killed many more of their own people than the Nazis
I really don't want to defend the GDR here, but that is hardly the case. The Nazis killed alone for political reasons approx. 1000 to 1200 German people in the first year after taking power. That is more than the SED executed during its' entire existence. And the number rose particulary in the last years of the war.
overthrown by their people in the end because of that.
Where was this the case? The SU and by extension the GDR fell because they were unwilling to resort to violence and implement a "Chinese solution" in 1989. Perhaps it would not have saved them anyway, but excessive violence against their own people did not lead to their downfall, the opposite did. The Nazis would have just executed the ringleaders early on when the first protesters assembled and be done with it.