From the perspective of stills photography, I'd say that the 6D suits your needs since your stated subjects don't really require the autofocus system of the 5D Mark III. However, I don't think that the 6D will ever come close to matching the 5D Mark III when it comes to raw video - at least based on the ML hack as it is currently implemented. The main bottleneck there is the write speed since the ML firmware is simply writing the liveview feed in the buffer rather than using the Digic 5 to process it. Write speed on the 6D is limited by its use of SD card, and 1080p raw seems to require the write speeds of UDMA 7 CF cards, which are available in the 5D Mark III but not the 6D. So I guess the question comes down to whether raw video is really something you want to explore. The image quality from raw is pretty spectacular, but it does come with a price in terms of workflow and storage space. Then again, the 5D Mark III is capable of the stills requirements you stated, but the 6D is likely not capable of 1080p raw. So it comes down to how important that is to you, and how much you're willing to spend.
Both are great cameras.