PNG always has stronger compression capabilities. There are a few fundamental exceptions where GIF is [significantly] smaller in size than PNG, like single-pixel blocks or basic resource textures. Although local loading times for PNG renders may be slower than GIF, if the compression is heavy, smaller file size seems to compromise this disadvantage for online images where browsers support it.
There actually is a version of JPEG where encoding is lossless, but it's a custom format used by Jasc image software. (Photoshop doesn't support nearly as many formats and storage techniques. :P) Not to mention it's more similar to Windows bitmap renders than PNG compression.
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