Advantage G7x: Touch screen, more focal length, significantly more workable, better handling / operation
Advantage RX100 III: viewfinder (which I do not need to), Camera Apps and slightly better sharpness at close range.
With a focal length of 24mm delivers RX100III slightly better pictures, the G7x supplies from the intermediate focal length nicer / brighter pictures. For 700 euros you can probably assume that you get a good quality camera, I had this impression during the Sony but not really. The viewfinder does not fit exactly into the case, the folding screen does not make strong impression. The Canon however, is perfectly finished.
The aperture advantage of 1.8 is at the Sony quickly put even at 30mm only is the iris 2.8 available. The Canon I at a focal length of 50mm is still 2.2 and only from a focal length of 70mm 2.8.
Negative evaluate the Canon is the battery. Approximately 220 pictures are simply too little and the replacement battery will cost at least 69, -Euro. In addition, there will probably be no replicas, Canon has managed to install a barrier here. Sony advantage.
Unfortunately, you can not charge the battery in the camera, everyone in the Sony without problems (as is also provided), even with a rechargeable battery pack!
Conclusion: 700, - Euro, the camera is clearly not worth the rather G7x buy a spare battery and continue for approximately 160, - Euro save. The image quality of G7x is not under laboratory conditions absolutely equivalent, partly even better !!! The touch panel and the longer focal length is not too shabby!