Armchair advice, because I've never published a single video that I've shot (!) but whichever device you use, lock everything possible: aperture, shutter speed, focus and white balance (don't forget the WB!). if you are in a controlled environment then that's easier than out-and-about, but it doesn't matter if it's 480p or 4K - if your AF goes hunting during a talking head shot then it'll be painful to watch, so lock off as much as makes sense for your environment.
Keeping to 180 degree shutters (ie: 1/60s for 30fps) is nice if you can, but don't stress too much about that, and don't worry about getting an exact 1/48 or 1/50 for 24/25fps) as this will will give a more traditionally film-like feel to the final video (we've been unconsciously taught to expect motion blur). Using a higher shutter speed (ie: 1/250s at 24fps) makes it feel more soap-opera like.
So pick the device that gives you the most control over the above, and then you'll find it easier to get the feel you want in the final edit.
You will want to look at the mic settings - auto might be fine, but again, if you are in a controlled environment you might want to fix the audio gain so that any background noise is minimised - test things out for whatever your expected loudness will be during the shoot, and for a quick overview, make sure you're not going above +3dB (keep to 0 as a peak if you can) and you'll avoid distortion. There are tricks you can play to give yourself a safety track by recoding one channel louder than the other, and then sorting it out in the edit, but audio is a whole new rabbit hole to go down !
Don't be afraid to use both: maybe the 6D for talking head to camera, and then the mobile for b-roll close-ups of whatever you're talking about - that will depend a lot on what your channel aim is, and how your style will develop. A mobile is far, far simpler to use as an overhead 'desk view' device than a DSLR simply due to the weight and size of it.
I've used Filmic Pro (on Apple devices) and it is awesome for configurability, but there's no need to go splashing out on that until you've tried out the default mobile video app, and if that offer enough config then just go with it.
If it comes down to it, then which one lets you setup the view in the way you like best ? If the mobile fits the room and view better, just go for it with that.