> Fuji was making point-and-shoot cameras with lower megapixels but superior image quality since '05

Could you provide some references for this, please?

Not because I disbelieve you, but for the opposite reason. I have an aging low-megapixel Fuji which appears to take better pictures than much 'better spec' cameras owned by my friends. I'd like a replacement, but I don't want to lose image quality.