Making comparisons between currencies and blockchain systems is often a mistaken idea. Why? Because they're different solutions to different problems. Each of these two systems is based on its own separate security model. If we're talking about decentralized systems, and keep that 'decentralized' idea front of mind, then the most important thing that's worth mentioning is consensus. Of course, there are many kinds of consensus, of which the two most popular types are known as PoW (Proof of Work) and PoS (Proof of Stake). People often claim that one kind of consensus is better than another – but here, again, there are different solutions which fit different situations. Even so, it's clear that within one kind, there could be better or worse options. There's been very little written about when it's better to deploy a particular kind of consensus – which helps foster the misconception that you can take bitcoin's or ether’s codebase – and just use it for your own use-case? And there's even less written about how to classify kinds of consensus.
In practice, this sort of situation suggests that if someone plans designing a national digital currency, they use a bitcoin fork as the template (I've come across such cases). In this case it's not clear who the miners are, or why we even need them.
Let's look at a different example. Some people call Ripple a centralized blockchain. In fact they're right, in the case of a specific company which controls the validators network – although wrong when referring to the underlying technology.
Any kind of 'private blockchain' (a mistaken term, in my view – but I'm forced to use it, otherwise people are going to get disoriented) has a stigma to it. They are centralized, no-one's responsible, they don't differ in any way from MySQL (the open data-management system). Yet again, in the majority of cases this isn't fair – it's just that the system-builder never explained the security system, but critics didn't understand this.
At this point I'll try to explain what issue is solved by each consensus – in the plainest language I can muster.
Multisignature/Byzantine Fault Tolerance (BFT). These algorithms are primarily used for achieving consensus among a limited group of people (In the case of multisig, between individuals – or in the case of BFT, between dozens of people, most usually equals). It makes sense to use them when all the people in the process know each other, and the list of those individuals doesn't change often. One example would be voting among the inhabitants of a building on collectively-organized repairs.
PoS – voting by stake (or by percentage of ownership). This is very similar to voting among shareholders in a company –whoever holds the largest slice of the pie will get the most say on how decisions are made. The specific quorum for achieving consensus can vary according to the company concerned. Some may require a simple majority (51%), others might demand a two-thirds majority, and there could even be those who require a unanimous 100%. This is an issue decided by PoI (proof of importance) and DPoS (delegated proof of stake), when small-scale shareholders choose a Board of Directors as their representatives.
Federated Byzantine Agreement (FBA), which was first introduced by Ripple, and then modified by Stellar, permits reaching consensus among large numbers of participants who don't know each other personally, and in situations when the total number of participants may not even be known. Each participant extends to trust to only a limited (by number) group of other participants, and therefore achieves consensus only amongst a narrow circle. However, since each of these circles has some element of overlap with others, it's possible to achieve overall consensus. There are not, however, many examples of such situations in real life – models might include sowing the seeds of revolution, when people spread the word mouth-to-mouth, and infect others with their enthusiasm.
PoW owes its popularity to cryptocurrencies (it was originally presented as a journal article in 1993, and then first coined and formalized in a scientific study in 1999), and is certainly the most complicated to explain. In PoW, all of the participants remain anonymous, don't extend trust to each other, and their total number is unlimited.
Imagine if people, instead of competing with each other (or making war on each other) they'd instead be numbered by counters – and decisions would be taken on the basis of the polling. Bear in mind, at each round of decision-making people wouldn't be opposing each other, but instead opposing an imaginary goal – and whoever comes out winning decides the consensus for that round, and walks off with all the rewards. Whoever has the greater fire-power will win most often – and thus will most often make decisions for the entire network. All of the participants will be working on building up their strength – and this can lead to an 'arms race'. Obviously, it's possible for a part or section of the participants to opt to leave entirely, and set up their own separate game (in other words, a 'fork').
If we try to classify all these forms of consensus, there are two primary criteria (in my own subjective view – there could perhaps be other ways of classifying them), and these are (i) the anonymity of each validator, and (ii) extending trust to a specific validator.
Now it would make sense to compare systems within groups. Of course, there will also be some subgroups – but at least there won't be utter confusion.