I'm afraid I'm with AJ here. The social aspects of Flickr -- in particular discovery -- and the network effect mean that I don't think that OpenPhoto is an adequate comparator yet.
Instagram and Flickr (and Facebook and Picasa and so on) are all cloud-hosted central locations where you can go and see other users' photos. Even if most users were able to deal with the idea of self-hosting (which they're not, ignoring that it's a very retrograde step, taking us back to a decade ago), this would not meet most users' needs.
The utility of everything being in one (or two) place(s) is what will be the deal-breaker. Blogs don't get the traffic that they used to; I can't believe that self-hosted photo galleries would.