Compress video while keeping details
While watching the examples it struck me that your video is stuttering as it is over the top with MBPS (23 MB per sec). So I would address your compression scheme first. I recommend that you consider rending your work in mp4 with 5 MB to 10 MB per sec. Here is the recommended video and audio compression as set by the folks at Vimeo for optimizing presentation on their site:

https://vimeo.com/help/compression

Another issue your video example is facing is that the GoPro does not have manual exposure controls. In your example, I see the bike going through bright areas and dark areas rapidly hence quick changes of exposure from the GoPro auto exposure. While the Red Bull example, shows the bikes in a stable light situation that does not force the GoPro to make wide adjustments. The solution to this problem is to either use a camera that offers manual exposure or shoot scenes that are evenly lit so they do not challenge the auto exposure to make big changes. Also, since the GoPro offers you at least a choice of Spot or Center Weighted auto exposure you might explore how one or the other might help expose the scenes more evenly.