Here is some good info regarding the hero3 blacks modes.
http://abekislevitz.com/understanding-your-new-gopro/
The way the fov modes work are as a sensor crop for lower fov but as the full sensor is 3840x2880 in 4:3 ratio the cropped modes arent blowing up pixels just using pixel binning or interpolation.
1920x1080p in wide medium and narrow modes all have the same amount of pixels but they are gathered from more pixels off the sensor in the wide modes where the narrow mode is pretty much just the central 1920x1080 pixels.
If shooting 1080p wide then cropping you will lose image quality compared to shooting in medium or narrow modes. If you shoot in 4k then cropping will be more or less the same as what the camera does itself but the 4k mode is only limited to 15p. 2.7k 2716x1524 does allow for a bit of room in post to crop and not lose image quality as much. Any time you zoom more then 100% you are losing quality as you are simply making pixels larger. Using a higher res source and cropping to lower res allows for zoom with minimal quality loss.
Reading Abes post he describes the different modes pro's and cons as even modes in the same res and fov use different methods of binning or interpolation to get the final image. The higher frame rates are limited to how much pixel processing can be done and so tend to be a little lower quality and also faster frame rates increase shutter speeds reducing low light performance. The wide modes tend to have the best image quality especially in the slower frame rates as these use the most sensor area and blend mulitple pixels into one, some other faster modes will bin the extra pixels rather then blend them which reduces image quality.
Now if as rumoured in the next gopro we get high bitrate 4k30 video or 2.7k60 this will allow you to use post zoom and crop when exporting to 1080p with minimal quality loss. You can shoot wide and crop to narrow the same as the camera does in the hero3 black, also 4k scaled down to 1080p will generally be better then what the camera can do itself in real time so image quality is going to be better at full fov or zoomed. This is what the biggest advantage of shooting in 4k30 is not necessarily to shoot in 4k for a 4k display as these are still very expensive and not very common.