After testing out a couple of the different HFR (high frame rates) with the Sony RX10 Mark II, the 240fps setting looked very usable. Today I went around shooting random samples with just this one setting.
Prior to shooting in 240fps (or any HFR mode), you have to prepare the camera into 'Standby Mode'. Once the camera is in Standy, you can't adjust any settings (aperture, zoom, ISO, etc), and you can't adjust focus. So it's a bit tricky especially when working handheld.
Unlike the 120fps in which you can shoot all day, the 240fps will give you about 1 second of recording (maybe shorter). After that brief second, it takes several seconds to save the recording to the SDXC card. You really have to time your shot to fit into that one second of recording.
I still think the GH4 is capable of producing better footage (especially in low light), but the RX10MKII offers a bunch of features and some not found with a GH4. To match the focal range on a GH4 with what is available in the RX10MKII, I would have had to bring my 12-35mm F/2.8 OIS + 35mm-100mm F/2.8 OIS lenses. When traveling or on vacation, it's just easier to work with one lens.
Both cameras will give you 4K internal recording, but the GH4 only offers up to 96fps while the RX10MKII can shoot 120fps all day + options for up to 960fps (240fps is probably the max I would use). I also enjoy having an ND Filter option built in with the RX10 MKII instead of having to carry ND filters.
Both cameras will offer 4K Internal recording and the stabilized zoom lens on this RX10MKII allows you to shoot very stable footage so that you don't always need a monopod or tripod. The RX10 even offers a de-clicked aperture ring so that you can adjust exposures on the fly. There's a microphone input and Headphone output as well, so you can use this as a full run-gun event or documentary camera.
The footage in the video above was shot in SLOG2 mostly ISO 1000 - ISO 2000. I'm still not happy about coloring SLOG2 on this camera (it's different than A7s, but I think eventually I'll find the right settings as I keep trying.