As I am not you, I cannot know what will be perfect for you. What I can do is explain what I would do for myself and try to explain why I would make those decisions. Hopefully by doing this, I can give you enough information you can make your decision; which will probably be different than what I would do.
So for me, if I wanted a compact camera for really good image quality, I would probably get either an EOS-M or a powershot G series.
Both of which are probably out of your budget; with the G being too bulky. While powershots can be good cameras, with the exception of the G series I tend to think of the image quality as relatively in the ball park of each other. Battery life can vary, so I would not base a decsion on that. The last time I got a powershot for myself it was a powershot A10 from 2001/2002. Even then it was a gift that got me into photography. Upgraded from that to a rebel XTi/400D, and from there to a 5DIII.
Humn, just realize that waiting 6 years before I do a massive upgrade in body is not abnormal for me. Good to know.
Anyways, with all that said, from what you have described I would tend to go with the S110. Canon tends to use the same sensor in their S series as their G series, and I'm not sure I would want to go back to just jpg. A nice rule of thumb is any zoom over 5x will be a compromise in image quality. If you want a zoom over 5x, go for a 20x (SX280 HS) or something similar; and recognize it is a compromise. Also, having more light means you can have a faster shutter speed so your subjects are not as blury due to slight movement. Increasing the light coming in decreases the amount of time to wait for the light to get to a certain point. Also, just because you may not use the camera open all the way all the time does not mean it could not be handy.
This is not to say the Ixus 255 is a bad camera, and it may be the perfect compromise for you. The only thing I really see going for it is the 10x zoom, and at that point I would prefer a 20x or more. If you are just going to have jpg photos, I don't think you will be pixel peeping and squeezing every last capability out of the camera, which means you will probably not notice much difference between the cameras. As I said, the Ixus 255 might be the best compromise for you.
Not sure if this helped or not.
Canon 5DIII, Rebel XTi/400D
Canon EF 16-35mm f/2.8L II, 24-105mm f/4L, 50mm f/1.4, 70-300mm f/4-5.6 DO, 85mm f/1.8
Sigma 150mm F2.8 EX Macro
Sigma 10-20mm f/4-5.6 EX, Canon EF-S 18-55mm f/3.5-5.6 II
Canon 430EX II
Opteka 13mm, 21mm, and 31mm extension tubes
Vivitar 50mm f/1.8 for OM System