Re:Maybe you can help me with this... (Score 1)

Maybe this will help.

1. PNG is lossless, so image quality is always perfect (not merely "surprising").
2. JPG is lossy, so it's allowed to degrade image quality to get better compression (and this is something you can tune when you do the compression).
3. GIF is lossless also, but it doesn't compress as well as PNG, usually.

So, to answer your questions...

Can you get amazing compression rates with PNG? Yes, but this depends on your definition of "amazing."

How do I achieve better compression than GIF or JPG? Pngcrush will take an existing PNG and make it as small as possible with no loss of quality.

How can I get PNG to perform consistently better than GIF or JPG? You can't. As you observe, it depends on the image. A photograph will pretty much always compress better with JPG (which loses quality, remember). PNG will do better on an artificial image such as a cartoon or a screen capture.

Hope this helps.