I cannot speak from the videographer end (I do shoot DSLR video, but it is not my focus), but after having shot my first business event (primarily stills) with my new 6D along with my 5DII last night, I would gladly exchange my 5DMKII for a second 6D today.
1) Coming out of standby. When I shoot events, I keep the camera(s) on and let them sleep. The 6D is (in my unscientific testing) somewhere between 2-3 times faster in coming out of sleep mode. The 5DII was noticeably slower. This is a big deal when a crucial shot in unfolding and you are waiting for your camera to come alive.
2) Snappier autofocus and less shutter lag. I actually had the snappier lens on the 5DII (135L) vs. the Tamron 24-70 VC on the 6D), but while the 135L focuses faster, I still felt my overall focus to capture time was better with the 6D. I had never really known the shutter lag of the 5DII until I shot my 6D. It seems to snap while you are still thinking about snapping.
3) ISO performance. I was shooting in 2500-3200 range most of the evening. The noise level and overall IQ is noticeably superior in the 6D, not to mention the color is superior.
For the kind of work I do (events, weddings, portraiture, then fine art/landscapes), the 6D promises to be a great performer. I am really excited about it.