https://download.wpsoftware.net/bitcoin/pos.pdf (skip ahead to costless simulation)
Anyone who tells you they know how cryptocurrencies are going to play out long term is blowing smoke up your arse.
The killer feature of bitcoin is that it's distributed. That has a lot of tradeoffs, because it's a fundamentally different way of doing electronic money. Bitcoin is shit for doing some things, but hey, so are SWIFT transactions. Bitcoin uses more electricity than AMEX but it pulps less trees than paper notes, pick your poison. It's all about having a broad set of tools in the toolbox, so you can pick the right one for the job. The reason bitcoin has value is because it offers a unique set of tradeoffs that can do /some/ jobs better than all prior financial tools.
A lot of people are going to spend a lot of time trying to find ways to fix the negative parts of the tradeoff, but thus far the fixes that have been proposed generally involve making the network more centralized and/or accepting a certain number of trusted actors in the system.
The thing is, if you're going to have a centralized system that maybe hinges on trusted actors, you might as well use an actual bank. Banks have tradeoffs as well and there are certainly downsides to them, but one of the pros is that a bank operates under regulation that creates legal ramifications if it breaches it's trust responsibilities (at least in theory). Why would anyone want a version of bitcoin that requires you to trust that you won't get lied to when you bring a new node online to join the network?
So my guess (and it is just a guess) is that proof of stake systems will not overtake bitcoin in market value /unless/ they become subject to government regulation that enforces trust through threat of arms (police kicking down your door). Without that, their inherent bias towards creeping centralization will cause them to hit a value plateau.
They are all a bunch of agenda-pushing hacks.