Well, this is not a huge test, it’s just a small thing I felt I needed to do.

After a lot of playing and shooting stuff with all the generations of my GoPro cameras I felt I would get more technical on the subject so I tested to see what exactly happens when you select the different FOV options from the camera’s menu.

It looks like you get rid of the fish-eye effect only shooting “narrow”, but here the noise on the image is disturbing from my point of view. Probably things get better in natural daylight where the camera doesn’t have to compensate the low light.

The test was shot at 1080p and please note that I used a GoPro Hero 2.
UPDATE:
In the meantime (november 2015) I own a GoPro Hero 4 Black, and I got wiser:)
I shoot wide – as it’s native – at the highest resolution – 4K – and then de-fish in post. This lens correction option is a built in plugin in the latest Adobe Premiere Pro versions.