Thanks for your help.
But I really do not get a grip of this. Its so confusing. I tried to change the color settings in After Effects… in Projects settings/ color settings I changed to 16bit color, then the video output became lighter, but when I render to quicktime animation, that file looks even much more bright than the video output in After Effects.
I want the video output in After Effects to look the same as the quicktime animation file I render from AE. It seems to be inpossible??