HTC lagged behind with 2160p video adoption - the HTC One and One (M8) didn't have the resolution for it (a 2160p frame is 8MP, they had 4MP cameras), so it was only the One M9 last year that brought the company into the world of 4K. Meanwhile, LG and Samsung have several years of experience on the matter.
The HTC 10 records the 2160p videos at a slightly higher bitrate - 56Mbps, compared to 48Mbps for the other two. It also offers an interesting option - lossless audio, FLAC. It's available for both 1080p and 2160p videos and replaces the already good 192Kbps/48kHz lossy option (16-bit AAC).
The FLAC is captured in an impressive 24-bit 96kHz format, what could be called "studio quality." So the limiting factor here is the quality of the microphones, not the audio format (unlike Apple, which still uses mono). And unfortunately for HTC, those don't live up to promises, to our ears the LG and Samsung audio sounds better.
Moving on to video quality. Here the HTC 10 impresses with a high dynamic range, allowing it to preserve both highlights and shadows. The footage has a low contrast, though, giving it a washed out look. The problem with noise in the shadows appears again.
The LG G5 videos have pleasing colors and a punchy contrast, but there's noticeable underexposure in the shadowy areas. Still, overall the image looks sharp and rich in detail. One annoying thing we noticed is a "pulsation" (look at the road surface). It seems to be caused by compression and it's periodic nature makes it noticeable.
The Samsung Galaxy S7 edge video is softer, not as soft as the HTC, though, and the higher contrast makes the video look better. The Samsung maintained perfect focus throughout videos, the LG G5 was fairly stable (with minor twitches here and there) and the HTC 10 did a lot of focus hunting.
Winner: LG G5. Unexpectedly, it came out at the bottom for dynamic range, but it produced the most detailed videos with good colors and contrast. The Samsung Galaxy S7 edge does a solid job (more stable focus, especially compared to the HTC).
In 1080p mode only the Galaxy S7 offers a 60fps mode, but we'll stick with 30fps anyway as the most popular option.
The HTC 10 maintains its dynamic range advantage, but again videos could use a bump in contrast.
A bigger issue is that the field of view narrows significantly, so changing the video resolution would also require taking a few steps back to frame the scene the same way. The other two also shrink their FoV when going down in resolution, but to a much lesser extent.
The levels of resolved detail even out. LG G5 footage appears more detailed, but that's largely thanks to the sharpening and contrast boost rather than resolving power.
The Galaxy S7 edge is more restrained with that kind of image processing (the tables are turned compared to still images).
Winner: Samsung Galaxy S7 edge. With resolved detail on par, the better handling of dark areas of the scene as well as the more restrained processing give the S7 a bump. Stable focus and 60fps option help too.
All three phones offer a slow-mo video option at 720p resolution. The Galaxy S7 edge records at 240fps, while the other two at half that - 120fps. Thanks in part to the higher frame rate, the S7 edge produced the smoothest videos by a wide margin, while the LG G5 showed us really choppy video with no fluidity. HTC 10's video was smoother, but not all that slow.
Winner: Samsung Galaxy S7 edge. The higher frame rate allowed the phone to create smooth slow motion, while the other two left a lot to be desired.