On the left is the original footage from the DJI Naza F450 GoPro. On the right is the "stabilised" version. By uploading the original to YouTube, applying the stabilise, then downloading the MP4 and running it back through YouTube you're able to see a side by side comparison.
The stabilised filter has some funny side effects where it appears as though the video is suddenly zoomed in and out. The blurriness of the RHS probably isn't a fair representation because that side has been uploaded, compressed, and downloaded.
The process does crop the video slightly and uses the edges as a buffer to remove the sudden movements from side to side or up and down.
The videos are in pretty good time sync but you may notice the RHS looks like it's behind the LHS. This lag is due to the smoothing effect of the filter and sudden movements take a little bit more time to catch-up with the RHS.
I've since changed the mount that the GoPro uses and without any post-processing the video is quite smooth. It will be interesting to see how smooth a video would look from the new mount after applying the stabilise filter.
Overall for this type of video, the stabilise filter does a pretty good job.