I really didn't want to get into this they are two completely different cameras and my thought patterns have been the following: Video = Sony A6500, Stills: Canon 6D MKII. After having used both of them, I'm a bit more confused than usual and can't really pick one over the other and label it as "better for video". They both offer certain advantages over the other. Let's look at a few. The Sony is stabilized and offers 4K, both of which are no doubt biggies for certain people, For one don't care much for 4K at the moment as storage and computing power for editing are a bit of an issue. There is still stabilization and 120fps, which creates butter smooth slow motion clips that look pretty good. The Sony has OK autofocus, not great and no tilty-flippy screen which make it a less than ideal vlogging machine. As far as picture quality goes, I think the sony might product better images using the same lens and same lighting, but some might argue... Neither of these cameras have headphone jacks which hasn't been an issue for me, but if you're trying to shoot light and don't want to use an external monitor, it could be annoying. Another thing about the Sony is the crop factor of 1.23X which makes even a 30mm lens pretty tight...I didn't really find it to be an issue with the kit 15-50mm lens, but I didn't really use that lens anyway as the Sigma 30mm F1.4 has been my favourite for a while but for vlogging, you'll need 10 feet long arms. Or a very small head.
Onto the Canon 6D MKII.... It shoots 60fps, or 30 in HDR mode @ 1080p. That's about it. Not to many settings for video, more like nothing really. Resolution, Framerate and that's about it....If using AF however the canon quickly becomes desired. The touch screen dual pixel autofocus is really neat and makes focusing a breeze.And there is another cruically important thing. Canon colours. I find the colours from the canon more please to the eye.
Look at both samples and see for yourself.
I personally prefer the look of the canon if not using log on the Sony. With the Canon, you don't have to worry about log, because it doesn't have it. Just like 90% of other Sony menu items, but it looks good..... In both cases you're limited to 29.9 minutes of recording which isn't an issue in the case of the Sony, because it might overheat well before you hit that limit.
The purpose here is not to steer anyone in either direction, but just to give an unbiased feedback on both cameras. They are both great, just depends on which one you prefer.