For me, when viewing a picture or movie, I want to see images / video reproduced to a color scale that is true to life, emulating the experience of looking through the window, and that is generally far better performed by IPS than by AMOLED displays. Black levels are also important to me, and are more accurately depicted by AMOLED, but that doesn't carry as much weight in my preferences.
But there is no right or wrong answer, other than to say that the best looking of these screens is the one that is best looking to the individual. It boils down to whether you want something to be an accurate representation of the original it is trying to reproduce, or prefer an 'enhanced' recreation (and while I'm of the former type visually, I'm of the latter type aurally).