Looks like there is quite a lot of Chroma NR being applied to this picture. ISO 6400 with absolutely no NR looks very messy, but it does clean up quite nicely, like in this picture.
Here is the shot as it was taken, no profile correction, no strong contrast curve, and no edit to her eyes. Just like the last time I posted it there is NO noise reduction at all. This was shot in RAW with the faithful picture style.
ISO 6400 only looks poor with the 5DIII if you are under exposing. In this case I slowed the shutter to 1/50th, and had the image properly exposed in camera at ISO 6400. Under exposing at any ISO and then using Lightroom to make up for it will make any file look like junk.
The worst of noise lives where images are improperly exposed. I've only shot with the Mark II momentarily so I can't speak to how it performs, but my T3i behaved just exactly the same. Of course it can't shoot at 6400 and get a usable file in any sort of light.... but I am able to make usable files at 3200 with it.