MFT cameras don't share the same wide field of view as a full frame DSLR. In addition the 4K Video setting on the Panasonic DMC-GH4 is further cropped in when compared to it's own 1080p setting.
One benefit to shooting 4K video is the extra resolution that will allow you to recompose, level a shot, or even zoom in to frame when outputting to 1080p. Seeing how my Rokinon 7.5mm Fisheye lens became less 'fisheye-like' with the 4K crop, I was also curious about using the extra resolution to correct the remaining distortion and finally outputting to 1080p. Nothing new as many users have 'de-fished' the Ultra Wide look from early GoPro cameras. I attempted to DeFish a BlackMagic Pocket Cinema Camera Clip with my fisheye lens that ended up looking great, but 1080p can only be stretched so far.
Here's a video showing different crop factors between 1080p using the Panasonic 12-35mm F/2.8 (@12mm) and the Rokinon 7.5mm MFT Fisheye Lens.
My tests with the GH4 4K Video show that the image is far from perfect, but far better when attempting to defish from a 1080p file. There's an obvious loss of sharpness towards the edges if you're really nit picky, but in many cases where you have to work in very tight situations with a GH4, taking advantage of the extra resolution in 4K is a good option. (BTW no sharpening has been done in post in this video)