I feel that the point people miss at first glance with Flickr is that it's not just a "site", nor even a "Web 2.0 application" - it's a platform.
To me it's analogous to "why should I choose a Pocket PC over a programmable calculator?" - because you know that you and others can extend and adapt the tool to do things that the designers never intended.
People want that kind of platform remixability. You would not believe the number of people that have mailed me asking for a port of FlickrExport to other photo hosting services. Flickr's already there and doing it, with deep APIs, not just a form that you can POST to from a client.