I can't talk from experience regarding 4K to 2K video, but everything I read and see says there is indeed an image quality benefit to downsampling to 1080 Vs native 1080, at least with these large pixel count sensors.
See Gordon Laing's samples here: http://www.cameralabs.com/reviews/Panasonic_Lumix_GH4/
Would anyone else care to chime in as far as best post practice is concerned?
Here is what Nick Driftwood briefly says about his sample vid :
"Here's a 14 second sampler from my previous Panasonic GH4 C4K (cinema 4K 4096x2160) video upload resampled by a little routine programmed by Thomas Worth at Rarevision. Employing 4K 4:2:0 to 2K 4:4:4 pixel summing Worth's code offers true 10 bit data in the luminance channel and spits them out in separate DPX files (each DPX=17.7MB) ready for grading/editing/rejoining/conversion to pro res, etc."http://vimeo.com/91573346