I've seen a 4K (Original as designated at the bottom of the screen) video from the Acer Liquid S2 on YouTube and it showed similar symptoms as the Note 3's 4K did: bad stuttering and trailing in low to medium light scenes, noticeable artifacts in scenes with movement and much detail etc. I have no idea how those videos would have looked on a true 4K monitor, maybe better maybe worse as the closest I had to view them was a Macbook Pro's small 3K display.
In static scenes or scenes with barely a movement, the differences between those videos's 4K and 1080p versions were noticeable but not much. However once the cameras started to move or pan around the whole image started falling apart. It would be interesting to test shoot each specific 4K-capable smartphone in both 4K and 1080p or even 720p modes in exactly the same scene and conditions to see if 4K is too far a stretch for any of these phones or it's the hardware/software limitations that affect the video image from them in general.
The key requirements to make the video coming out of this first generation of 4K video taking devices look anything close to the true 4K image hyped up by the vendors would be for the shooter to hold the device as still as if it were on a tripod or steadycam AND with controlled movement of the subjects and background in the scene being shot. Neither are those a strength of the people who shoot videos on these devices nor typical conditions their videos are shot in.
So in the meantime I guess we have to make do with variable recording frame rates (as opposed to variable iris, shutter or filtering to control the exposure) , lens breathing (the annoying zoom-like effect when the lens refocuses), rolling shutter, wobbling, jelloing artifacts, blocky and smearing artifacts when there is movement in the scene which are normally caused by too low the bit rates or the inability of the IP to keep up, the shakiness because of ineffective or non-existent stabilization system, and the list goes on.