For me, I try (emphasis on try) to re-create the image as I saw it when I shot it. That means both visually and emotionally to me. The camera doesn't work as well as our eyes & brain (even when shooting RAW) so it does take some work to get the image to come close what I first experienced before tripping the shutter. Sometimes it's more work than others in terms of post-processing.
The best images have the right combination of artistry and reality. Can't say that I've ever achieved this myself though.
Great photographs are never taken they are created.