One of the issues with working any new camera into a production work flow is that it doesn't match your existing 'A' camera. GoPro are still in the infancy stages of providing a tweak-able camera, but it's really work-able if you know what you're doing. My first call to action was to analyze the color science of this camera to which tone curve on the 5D mark II (and probably mark III as well) match best with the brand new GoPro "Protune" setting. The goal here is to get the footage to match close enough that post production goes much smoother. The goal is NOT necessarily how to get the best look out of the Hero 3 - that's an opinion more than anything else.
Let's start with a plot of the tone curves using the excellent DSC color calibration chart. The gray scale portion of the chart was cropped out of each image and the luma was graphed in Premier Pro. I chose the "Neutral" picture style because that's the most popular to use with HDSLR video. The plots below show the tone curve with the picture style contrast set from 0 to -4. What we see is that the contrast= -3 is the best fit to the GoPro Protune tone curve. It's not a perfect match, as you can see. The 5D mark II is crushing the blacks a bit more than the Hero 3. That's each to fix in post with a little luma curve adjustment.
The next logical investigation is what happens when you turn on Highlight Tone Priority on the Canon DLSR. This, in theory, should give you 1 additional stop in the highlights. I often use this outdoors in order to maintain highlights, like clouds and light colored buildings, a little better. Again, the contrast= -3 setting is the closest, but not as close as with Highlight Tone Priority turned off. The highlights are being rolled off a little better on the 5D mark II, so you're giving up matching in the highlights a little.
Next I'll be looking at the color matching. That might take a bit of tweaking. The Hero 3 Black Edition has a "Cam Raw" setting, which is what I'm going to focus on since that seems like the best go-forward solution for outdoor filming with the camera. Stay tuned for part 2.