As Flash's programming language, ActionScript, continues to develop, so does its power, and the possibilities. For instance, it now includes limited video capabilities. So while Director is still the better choice for many applications, Flash is finding its place too. Indeed, combining the two is often the best answer.
Most of my work with Flash has been including animations within my Director work, for example controlling Flash-based maps within a Director framework for a travel CD. I have also incorporated Flash elements in HTML-based websites.