I don't have the current S110, but the previous one.
I bought the LX7 that you are considering. It is slightly bigger than the Canon, but in my opinion it has much better features. Select the regular focusing mode and the focusing is EXTREMELY fast. Select the macro mode, and of course, it is slower, but very snappy for a macro mode.
The f/1.4 lens is great in that it does its work without being noticed. But as soon as I try to go back to my Canon, that's when I realize that the f/1.4 has been keeping my image quality superb by using lower ISO speeds.
The LX7 outclasses the S110 by far. The S110 has basically stagnated with the same features all the way back to the S90.
The lens of the LX7 is much more substantial, and you will definitely want to use the cap-keeper to attach the lens cap to the strap eyelet since the lens cover is not an auto-retracting style, but an actual SLR-style lens cap.
Another thing is that the camera strap isn't a hand strap like the S110. It's an actual neck strap.
It's kind of awkward putting the camera into a belt pouch with an entire neck strap attached to it.
I might just swap out my old Canon hand strap and use it with the LX7.
There are some deals for the LX7 at $350 or lower. If you can find one of those, I would have no hesitations in recommending the LX7 as a much better buy.