Slightly modifying the command line by @izx, I got this:
ffmpeg -i in.mov -map_metadata -1 -c copy out.mov
The result is (again, checked with exiftool), a metadata record reduced from 81 to 52 lines. Note that you can't simply remove all metadata, some things will stay.
Note that the above command only copies the first audio, video, and subtitle streams. If you want to copy all streams, add the option -map 0:
ffmpeg -i in.mov -map_metadata -1 -c copy -map 0 out.mov
If you want to remove the newly added encoder field, add this to the command (before the output filename):
-fflags +bitexact -flags:v +bitexact -flags:a +bitexact
Thanks to @wisbucky for the hint.
If you want to actually change/overwrite a field, e.g. the generated title, you need to set:
-metadata title="Some Value"
However, I didn't get the creation date to change, which is strange because it seemed to work in the Ubuntu version. I posted on the FFmpeg mailing list, asking whether there were any updates or comments on that, but there was no answer.