I have a made in China go-pro knock off. It will record 1080p, but only at 30 frames per second. It works pretty well but the software is limited. If I mount the camera inverted, I need to use video editing software to flip the image, the camera has no options.
I bought my father the gopro hero4 silver for Christmas as he wanted one.
I chose that model for good picture quality and simplicity of use.
The hero4 silver has the touch screen back and viewfinder included(easy to turn off to save power). It will capture 1080 at 60 frames/second or 720 at 120 frames per second.
When looking at cameras, image quality is important, but you also have to think about frame rate; fast moving films will look choppy with lower rates (my HD camera takes great images, but autocrosses are somewhat choppy). A high frame rate will also allow you to slow the video down and have more images.
The description of image quality is similar to what is used on TV's: 720-1080 is modern HD, higher is better image quality (youtube has some side by side films if you want to see the image difference) 4k is pretty cool, but not common yet.
The camera's also seem to take pretty high quality still photos.
The downside of the hero4 silver is mounting: I haven't spent much time with it, but there is no standard camera mount on the camera itself: you have to place it in the waterproof case to mount. With the touch screen back and wifi connection, this is not a big deal (and keeps the camera somewhat more protected) BUT the cases seem to cut down on sound quality.
So there is that to think about.
For reference: this is me overdriving my hybrid at 720p (not greatest image camera can produce), but at 60 frames per second (what I would consider the minimum for action)
this is not a gopro, its my Chinese "action cam." crz
There are obviously more options beyond the top line gopro and a Chinese knock off, the gopro is however like the iphone of smartphones; its established with a good support base and easy to learn. The gopro even allows you to download a free video editing software program for your pc/mac.