I used the Lumix G 14mm f/2.5 lens on both cameras.
Both cameras were mounted to a Desmond Mini Dual Camera Bracket, typically used for stereo photography. On the lenses, I have used 46mm to 37mm step down rings as hoods. They do a good job of keeping the front lens elements safe from accidents, in my opinion, while also keeping out some stray light. If you want to use them, you also need a 37mm front lens cap.
We see that the GH4 has marginally less rolling shutter artefacts. This is probably because it has a faster 1080p video frame readout. By using the slow motion feature, the GH4 can read out 96 frames per second (in 1080p mode), while the GH3 could do maximum 60 fps.
Further, the GH4 has cleaner image quality in ISO 6400m which should come in handy for video recording for example in dark concert venues.
We see that the Lumix GH4 is not consistenly focusing faster during video recording, with the Lumix G 14mm f/2.5 lens. But it gets the focus the most correct most of the time.