1. Up until a few weeks (months) ago Facebook's iPhone app was complete shit. My younger highschool brother (and all his friends) who are not techies in any sense, always complained about how it sucks. One time I even asked them why they switched to Instagram, and they told me the app works much better than the Facebook app and it's a lot more simple to just post pics/browse. That brings me to my next point.
2. Facebook has grown to the point where it doesn't know what it wants to be. Kind of like myspace was trying to do everything, Facebook is in a similar position (except their products actually work). Instagram specializes in just photos, and makes it easy to use. There is no other crap to get in the way, you upload pics, like them, and comment on them. That's it. Twitter specializes in just short, to-the-point comments. Where does that leave Facebook?
3. Facebook is establishing itself as a kind of social media aggregate. When I post anything to twitter, instagram, or tumblr, it automatically gets posted to my Facebook. But I rarely ever post anything directly on Facebook. From my experience, nobody is leaving Facebook, they just use it less. And as a side not, I think Facebook's strongest features are Groups and Events, I use those two features more than anything else. It is so easy to create groups and invite people, it's awesome.
4. Instagram has cool photo filters that make it very easy to make your photos look "cool" and cover up any imperfections in the pictures. Take any shitty picture and apply a filter, all of a sudden it doesn't look too bad. Sure it looks generic, but it doesn't look like complete crap (most of the time).
Anyways, that's my take on fb/twitter/instagram.
The eventual winner in the space may well be whoever solves this: automatically figuring out which friends are more important to the user, making that measure invisible to users, adjusting it appropriately over time and then filtering to show everything from the most important as well as important updates from less important people while still allowing the user to see less important stuff from the less important people. The eventual winner could also be FB just on sheer forward momentum, size and how deep their hooks are into everyone.
I wonder if increasing bandwidth has also played a role in FB's declining engagement. FB was built as a pics and text based site but long term the trends will move away from this. Yeah it does video and music and everything else but they are stapled on. Over the past year I've watched my wife use FB less and less each night and things like skype and netflix more and more.
My usage patterns are quite different from yours. Facebook is my primary service. I don't post on Twitter at all, and I rarely even check it, but sometimes I'll retweet something. I have friends that use twitter a ton, but they're actually the few power users. The majority of my friends either don't have a twitter or never post at all.
I also use Instagram very sparingly. I have an account but that was just to see what the hype was all about. I've posted a couple of pictures but a majority of my pictures and albums go on Facebook, where I can tag my friends, and have the vast amount of my friends see it in their feeds. A lot of my friend do have Instagram account but either they use it a lot or they don't use it at all, so again, it varies between those extremes. Those that post their pictures to Instagram, also post their pictures to Facebook, and since Facebook owns Instagram, I feel like it's a win-win for them (driving traffic in both places). They also recently blocked out twitter, so there's that too.
I actually think people are using Facebook more than ever from what I've seen. It's trying to do everything, but at the same time, it's doing everything well. It's powerful, and all your friends are on it.
The iOS app used to suck but it's actually one of the best apps I've seen now. It's super duper fast and they are continually adding functionality to it. Combining the FB and Messenger apps was such an awesome change and I haven't heard people complain about the iOS app ever since the redesign. I still hear complaints about the Android one though, and they definitely are working on that.
So yeah, I think different types of people use these platforms in different ways, but at the core they're all using Facebook, and also Facebook Connect, so I don't think FB is having an identity crisis at all.
EDIT: Another point I'd like to make is that above I pointed out how a lot of users use services like Instagram or Twitter in an "All or Nothing" manner. However I think we can agree that people on Facebook use it on a much wider scale. However,the important thing is, you don't have clustering at the extremes. More importantly, you don't have the clustering at the "Nothing" end. There are some people who don't have Facebook, but those that do, tend to use it in SOME manner in varying degrees which works out to FB's advantage.
If true, it's not about pivoting, but figuring out how to connect with the relevant trend setters.