All three of the cameras produce sharp pictures.
The Canon S500 and the Sony P8 are classified as point-and-shoot cameras.
The Canon A80 is an intermediate camera, which means that it can function as a point-and-shoot camera but has many manual over-ride functions. The photographer that want to be able to have full control of his pictures would select this type of camera.
Many people are happy with not wanting to worry with all those functions and the point-and-shoot camera is for them.
The S500 costs about $150 more than the Sony P8 but gives you more megapixels.
Once you get your choices down to two or three cameras, it is time to visit a store and get your hands on each one. That will help you decide.
I'm looking for my 1st camera. I'd like one with sharp pictures, not too heavy, etc, and I can't decide between the Canon PowerShot S500, Canon PowerShot A80, or the Sony CyberShot DSC-P8.