Consider that a 'placed' product is like a background extra in a scene and 'integrated' product is like the star. The best job of product integration I've ever seen was in The Castaway where both FedEx and Wilson became characters in the telling of the story. We were so sad when Wilson floated away!
The James Bond series has been a veritable placement/integration franchise hitting both with skill and elegance. By the way, integration has an element usually lacking in placement--implied endorsement.
So here's a quiz: Was Manolo Blahnik placed or integrated into Sex and the City?