I am a portrait photographer, and I love the 6D. I find the increased dynamic range (over the 5DII) huge for smoother transitions on faces, and the AF is much more accurate for nailing those sharp eyes.
Plus, the Wi-Fi capability enable me to do this : http://www.dustinabbott.net/2013/02/i-believe-i-can-fly/, which would be near impossible with the 5DII by myself because of nailing the razor thin depth of field of the 135L wide open.
The WiFi is really awesome. To respond to the OP, I feel this is a such a subjective question that everyone is likely to have a different option here. All the best portrait photographers are likely to be using their own custom color profiles and tone curves. Since the 5D2 has been a favorite of portrait photographers for years, it's likely you are sampling their best work on flickr, and for the 6D you are just seeing the initial results - possibly from people who don't edit much or don't edit well - and aren't compressing the extra DR that the 6D offers. Also I find that the lens can have far greater effects than the sensor in terms of color rendition.
Honestly the biggest thing I'd be worried about with the 6D is the max x-sync speed. When using studio lights and a radio trigger, you are stuck at a max of 1/160. Which is a fair bit off of the 1/200 on the 5d2.
However, at the end of the day, I still chose the 6D for it's better DR, color depth, and overall more modern functionality (including its auto-focus and support for the Canon RT flashes).
I do find the images can be a little flat out of camera, but with a touch of post-processing they are quite nice.