Yeah as mentioned, Flickr was/is basically a more complicated version of Instagram without the hipster tinge.
Also, pretty sure PicPlz came before Instagram, and for a long time had more users (must suck to be those guys right now).
I kind of figure they had simplicity on their side, combined with an initial target market of niche/boutique/hipster/grunge/retro, and the cherry on the cake was Facebook seeing them as a growing competitor in the photo sharing biz (that would have also added a threat to the value of their upcoming IPO). /2c
Flickr is something completely different. It's basically a suite of fun things you can do with photos, and designed so that one activity leads into another - searching, commenting, groups, tagging, searching, curating, apps...
Flickr failed to get into mobile partially because of Yahoo's interference -- but perhaps our approach was too complex for mobile. In the early days of Flickr, it was incredibly absorbing - people would waste hours on the site, just like Facebook. But that may require a bigger screen and more free time than someone has when they are on the go.
It's not too complex for mobile, as proven by apps that aren't from Yahoo. (Yahoo's Flickr app is egregiously slow, almost as slow as FB's "HTML5" app.)
Yahoo should have purchased both FlickIt Pro and FlickStacker, perhaps changed them to white with a designer feel, and marketed them as Flickr Social and Flickr Pro. (Seems to me the two markets of users Flickr serves are people there for the photo community, and there for dealing with publishing high volumes of photos.)
FlickIt Pro opens to a "People" tab, with incredibly easy UI. This focus on people sets it apart.
FlickStacker is an incredibly full featured uploader and Flickr photo manager. I was able to post and manage ongoing full quality photo sets during a recent trip to Corsica using just my iPad and this app.
Flickr also should have worked with Apple to build a Flickr uploader built-in, as Apple did with Twitter. Twitter or Facebook is great for snapshots, while Flickr is for photography.
In addition to your analogy, I'd suggest that Flickr is to TwitPic as Photography is to Snapshots. The photography market gets overlooked (though 500px is moving in) but both pro and amateur creators appeal to Apple. Instagram and Facebook are not about photography, so Flickr could still own that term.
Today, I'd no longer argue for a button to "upload" to Flickr. I'd argue for pushing the Apple iCloud Photostream to a Flickr Photostream mirror set that users can rename, then letting Apple's native Camera or Photos app built-in share interface toggle the pre-uploaded photos' visibility to Family, Friends, and Public. This lets the sync happen in the cloud, decreases friction, and encourages more Pro accounts since users could run out of 200 free photos quickly.
Also, pretty sure PicPlz came before Instagram, and for a long time had more users (must suck to be those guys right now).
I kind of figure they had simplicity on their side, combined with an initial target market of niche/boutique/hipster/grunge/retro, and the cherry on the cake was Facebook seeing them as a growing competitor in the photo sharing biz (that would have also added a threat to the value of their upcoming IPO). /2c