Here is a description of a movement I see happening.
In Brief
Golem possibly seems like Segwit for Ethereum, acting like a big distrtibuted super computer protected by immutable Ethereum transactions and/or contracts thus spreading out computing cheaply.
Segwit improves or adds to Bitcoin by acting as or allowing another multi-purpose layer providing many cheap transations and possibly contracts. Both of these keep everything valid by putting verifying keys or snapshots on the immutable chain.
EOS claims to make use of distributed computing for a parallel-like etheruem. It also must have an efficient way to verify data and processes, while destributing computing all over the network. (And why not make use of every computer separately, possibly using a tree-like hashing system.)
This all reminds me of Koin, where chain verification and immutability is done by voting, meaning computer work can be reserved for an artificial quantum computer, which I suppose may include contract processing.
Everything koin-wise is done through messages, including goverance, voting and currency. This distributive-computing as mining, is separate but uses the network and is an opportunity for 'miners' to earn money. One pays a node for work to do, who distributes it out starwise to other nodes for help.
The koin message system when added to this separate computing system, is similar in principle to Ethereum (maybe with golem added, to cheapen computing). This is not my original thought, but if one is paying for computing anyway maybe immutability, processing and data storage may be all wrapped together.
The idea is very cheap immutable verification and computing for a competive price. This is then a foundation to more social systems. Ethereum is doing this already, in some ways.
Separating computing, disk storage and even networking to be cheaply accomplished along with encryption and immutab, provides a nice foundation similiar to Golem + Ethereum, Bitcoin + Segwit, and EOS.
To be clear, these are simply general ideas explained by various groups and there probably are huge technical differences. Some of these such as koin may still be in idea form.
Computer Work, Immutability and Leadership
Something to consider is the idea that one must have a long elegant chain to have an immutable place to certify things.(Did you know you can hash an image or file, and time-stamp it on immutable bitcoin. This proves data's existance at some point in time.)
So anyone can fork a chain, but chances are those mining for the original will stay with the longest, basically for lack of better options. If some who are mining have mined one fork, they will be motived to stay with it, since it grants them money. The bigger players having mined one chain will likely keep it going. After a while one chain will obivously be longest and most elegant or precious (having most work-time).
But what if someone keeps one chain going, believing that someday it will catch on. If it is smarter or better somehow, eventually lots of big players could make it catch up and overtake the original. The longer time passes, however, the more difficult and maybe less likely this becomes. But immutability is subject to such possiblities.
In the case of Ethereum a leader convinced miners to rewind and recompute the work-lattice. Since little time had passed and many big miners helped out, a shorter fork took over the longer. So leadership can influence, not just the combined desires of richest, biggest miners.
In a way proof of work is proof of stake, if those mining keep rewards a while and remain constant, especially on short run.
I suppose good energy or social standing behind a bitcoin or crypto may change things. People may be convinced to use a certain blockchain which is identified or discovered through real-world naming systems. It may be IP, domain name or legal name.
Soft Identity
So computer work leads to longest chain and the default 'best' option. Still leadership or social power have sway.
In the end, I believe most efficient immutable foundation may come from voting and user/node consistancy. I focus on proving identity in the real world, but a compromise is soft identity, where one is known by online behavior. ENS or other naming conventions can even give an address a name and a way of directing everyone to its changing IPs.
(ENS: By the way, the current auction idea is ok, but maybe names should not be revealed until after. It could be hidden in a private key, public key posted, then original names/ideas go to those who create them. If multiple people desire same name, whoever put up the most money gets it. No doubt all this is understood/considered by the ENS people.)