Plus, I don't know if you like it... But I kind of like Canon's picture at 100mm a bit more. The color seemed more natural.
Canon G7X
Sony RX100III
However, I acknowledge that color is subjected personal preference. That is why I kept insisting that both cameras are good, they each have what they are good at and what they are not. You would have to match your expectation to these information and choose which camera that suits you.
And from the website Steelman provided and what I have read before, it seemed that at wider angle, Canon's picture is not as sharp as the Sony, but at tele length, it is another story all together.
So in summary, both cameras are excellent.
1) The Sony produces excellent sharpness in their photo slightly better than Canon G7X.
2) Both have great AF, although some review site claim that Canon is a tag faster in good lighter, while Sony is better in darker area. Sony had a good EVF (love it or hated it, it is entirely up to individual). For me, the EVF is not needed, because it is small, I wear spectacle and it is not comfortable to mash the entire camera onto my face.
3) Both cameras are small... the Sony is a tad smaller, but really not a significant amount. The Sony had more accessories thus far going for it.
4) Sony had greater flexibility LCD with more angles to choose from so making some of the shots easier. The Canon can only flip upward and so pretty limited. However I do find a way of shooting overhead (and that is to shoot holding the camera upside down) but I still find Sony's vari-screen LCD better in this case.
5) The Canon had a great touch screen. Love it alot. Sony didn't. But it is also arguable on whether you need it or not.
6) Sony offer greater video mode, while Canon's one are pretty standard and at this time of age, it can be pretty boring.
7) Canon G7X is significantly cheaper as compared to Sony RX100III.
So there... although both cameras appeal to the same market, but clearly they have significant differences and it is up to users to gather these information and basing on what they need and want, then choose that camera that is closest to those needs.
Who knows... one might end up with a Ricoh GR, Nikon Coolpix A or the newest Panasonic LX100 (when it is released).