We've got a Fuji F40fd here... it's the wife's point-n-shoot. I'm not familiar with the A560 but it replaced her Canon SD600. The Fuji has better colors and much better low-light ability, but is slightly larger and the movie mode records at a lower bitrate. The Fuji also has the annoying tendency to shoot flash photos at ISO 800 when using the flash in Auto mode, which results in noisier pictures than if you force it to a lower ISO with the flash.
Not a perfect camera by any means but pretty good for its class.