EOS R

+ Colours
+ Ergonomics
+ Menus
+ RF Lenses + native performance with EF lenses
+ Canon EF - RF adaptor with ND filter
+ Video bitrates
+ DPAF

- 4k Crop
- Single card slot
- 720p 120fps
- Not much in the way of "cheap" native RF lenses

With the most recent 1.4 firmware the autofocus performance of the EOS R is exceptional. RF Lenses are amazing and quite innovative, the ef - rf adaptor with ND filter is very cool for videoguys, higher bitdepth gives you more push and pull in post for video work. There's no getting around 720p 120fps and the single card slot, thats a straight stupid hardware limitation, the crop in 4k can be fixed with a EF to RF speed booster putting the crop at ~ the 1DxIII crop, and nobody complains about that....

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A7III

+ No crop
+ 1080p 120fps
+ Higher burst rate
+ Dual card slot
+ Autofocus
+ Fairly well fleshed out native lens range
+ About a stop better low light performance

- Menus
- Ergonomics
- Colours
- Menus
- Video bitrates

There's nothing you can do about Sony's terrible menus. The ergonomics are potentially more a YMMV point. Colours can be worked around but require more effort and if you shoot internally you're stuck with 100mbps which isn't ideal, but an external recorder solves this problem. GMaster lenses are all excellent if conventional.

There is no wrong answer to this question, both camera's are capable of exceptional results and there is plenty of aftermarket support for external lighting and video rigs for both systems. Best thing you can do is visit your local camera store and spend a good chunk of time holding and playing with them and pick the one that's more comfortable (in your hands) or less frustrating you use, no point owning a camera that gives you hand cramps or you dont want to shoot because you're fighting with one aspect of it.

Or better yet, worry less about the body and choose a lens system to invest in, bodies will get better with every generation but lenses are forever.