It does not depend on 1080p but on frames per second and shutter speed
The gopro has a fixed aperture of f/2.8 shooting at 30fps it sets the shutter speed at 1/60
When it shoots at 60fps the shutter speed is set at 1/125 (note is the faster shutter speed that gives you the good motion not just more frames)
As you double the shutter speed you are halving the ambient light the gopro will therefore increase gain to compensate the loss of light: final result more noise in the picture
When there is a lot of light the increased frames per second push higher shutter speed this is a good thing as otherwise you get clipped highlights
Take into account that the gopro is a basic camera so it does not react quickly to exposure compensation and changing gain, for example in your pictures there is generally lack of light so the camera increases the gain and the picture is noisy
At some point you get close to something and the lights illuminate it all of a sudden there is now plenty of light, the gopro reduces the gain too slowly as it is a cheap device not really designed for situations with changing lights and you end up with clipped highlights. Note that a situation like that would create problems also to better cameras but as better cameras don't have fixed aperture they react faster
That also explains why people should be careful spending $1000s in lights as in caves and night dives you get plenty of clipped highlights because of the limitations of the camera
It costs 299 to 399 there is a reason for it!
