It's not.

The image quality is comparable to the Hero 3+, with no clear consensus as to which is better (eg [1],[2]). Sony uses the Zeiss lens as a selling point, but still can't do the 4K resolution of the GoPro.

GoPro's image quality is good enough for it not to be something that counts against it in almost any case. A quick look at some of the clips produced by GoPros will give enough evidence to convince most doubters.

GoPro usually wins because of a combination of things.

Firstly there is the form factor. Usually it is seen as a downside, but then you discover that the "wide & short" GoPro factor is the only one you can chest mount safely, and the only one you can helmet mount in the middle of a helmet. That's usually enough to counter any "form factor" arguments (although I'd like to see a "long narrow" GoPro - there are some cases where it is better too).

Then there is the ecosystem. You can get GoPro mounts for anything. Most competing cameras sell adaptors, but then you often run into the form factor problem - the more common "long narrow" form factor doesn't fit into the same space as "wide short".

Then there's the software. GoPro's software isn't fantastic, but it's mostly ok. Most of the competitors have pretty bad software.

[1] http://www.digitalrev.com/article/gopro-hero-3-vs-sony/Njk3M...

[2] http://www.usatoday.com/story/tech/personal/2013/08/31/perso...