There is no doubt about it: The SX510 HS produces better photos than the SX500 IS. Color performance is very good and they don't get muddy or washed-out-looking until you get up to ISO 1600.
Still, the 12-megapixel resolution isn't much help when it comes to enlarging and heavy cropping or poster-size prints. With the exception of close-ups taken at ISO 80, there's a bit too much in the way of noise and artifacts visible when photos are viewed at 100 percent (take a closer look and you can better see what I mean). This is the case with most small-sensor point-and-shoots, though, so if full-size quality is important to you, you'll want to move up to a large-sensor compact.
This slide and those that follow all have links to download the 12-megapixel version of each image. They are large files, though, so it may take several seconds for them to download.