If I had to choose one of these I would go for the G7 because of its tilting viewscreen. Another reason would be the On/Off switch on the S110. To quote a review
The button is tiny, the same color as the camera, awkwardly placed, and essentially flush with the camera’s top deck making it almost impossible to turn the camera either on or off easily.
I have a preference for on/off buttons (and safety catches) that come readily to hand and are easy to work. Against the G7 is that it does appear to be quite a bit bulkier than the S110, if that is a concern, and it is quite a bit more expensive.
At the end of the day it is how the camera comes to your hand and whether or not you 'fit' together, as well as its optical qualities. I cannot offer an opinion on the video, although both seem quite capable, because I almost never shoot video.
From a personal point of view I would not choose either of these because of the lack of an optical viewfinder but I have to admit that pocketable cameras with optical viewfinders are becoming very thin on the ground.