Before I begin this anolysis, I'd like to make note of two things:
I am taking into consideration only the experience of playing Fallout 4, not previous Fallout games or any outside canon sources. I am doing this because in contrasting these factions, I am basically asking "What ethical choice should the Sole Survivor make?"
The Minutemen are not going to largely factor into this, since they are unconditionally loyal and do not provoke a war with another faction without the Sole Survivor's decision to as general. Therefore, the Minutemen are not considered a faction for this purpose but rather the Sole Survivor's own followers (despite having a distinct ideology - to organize and assist the people of the Commonwealth, which a player's version of the Sole Survivor may not necessarily sympathize with in all cases). However, their impact will be mentioned at detail.
I've created a metric for this study, a scale of extremism, violence, authoritarianism, and deception. Authoritarianism applies to both the entire Commonwealth and the members of the faction, whereas deception scores higher depending the less transparent the faction is about their agenda to the Sole Survivor and others. Higher scores mean the faction is less ethical, though everything is arguably relative.
The Railroad
A useful starting point would be to address the question - Are the Brotherhood, Railroad, and Institute all unconditionally dedicated to the destruction of the other two? The answer is probably more accurately "almost" than yes, and the Railroad certainly complicates what would otherwise be an all-or-nothing situation. The Railroad is dedicated only to the liberation of synths. There is little indication that they would be concerned if the Brotherhood of Steel came to the Commonwealth only to exterminate super mutants and ghouls, or would oppose the Institute if they abandoned the production and retention of synths in favor of other scientific pursuits. The Railroad embraces rather than fears technology as evidence by their cause as well as the contributions of PAM and Tinker Tom among others.
Dissent is not forbidden by the Railroad, as Deacon states there are differing views on whether only gen. III synths should be saved or all synths - and there is cooperation regardless. The Railroad takes mainly a defensive stance - only striking at the Brotherhood when attacked and the Institute when their secrecy is compromised and an opportunity to free a massive number of synths arises. They accept violence as a necessity but without much apparent enthusiasm for killing people.
One ethically anolyzing the Railroad must first decide whether the cause of liberating synths is right or wrong. Ultimately it rests on how one defines personhood, but Fallout 4 does give every indication that synths are as sentient and self-aware as humans. If the cause to liberate sentient persons from slavery is deemed worthwhile, it then must be decided if it is worth it to destroy potentially valuable Institute technology and kill some to save many. Perhaps the most important question: If the Institute is indeed an oppressor and enslaver, how many people within the Institute are directly guilty of that, and how many deserve to die in order to free more synths? It is worth noting that by the Railroad choosing Z1's plan over Liam's, they may be sacrificing adherence to minimize violence in exchange for an opportunity to gain power and exert influence.
Finally, we must ask how the people of the Commonwealth fare under a victorious Railroad. We can likely conclude the people will have to deal with the consequences of Institute tech destroyed and a few potentially dangerous synths being set loose, otherwise the Railroad does not intend to interfere with anyone's liberty or take the lives of anyone not directly opposed to them.
Extremism Rating: 7
Violence Rating: 6
Authoritarian Rating: 3
Deception Rating: 4
The Institute
Shaun as a leader seems remarkably similar to Desdemona insofar as both seem to express the idea that they do not wish to harm anyone who doesn't harm them first, but are willing to use extreme force to remedy such a situation.
There is much rationalization within the Institute that synths are nothing more than machines and that they as creators are not responsible for the welfare of synths or potential harm caused to them or by them. The Institute is a polar opposite of the Railroad in another fashion: They believe synths should be sacrificed for the benefit of humanity where the Railroad sacrifices humans for the benefit of synths.
Shaun is a manipulative leader. He grants his parent increasing amounts of power in hopes of winning him over and is not swayed by dissent, but always has a calculated, rational counter to any concern of the Sole Survivor. Is Shaun egocentric and selfish? Hard to say. He gives off every indication that the Institute is much bigger than him as a person and that his life is insignificant by comparison, caring only about the future of the Institute on his deathbed rather than preserving his own life. There is a cult of personality around him though. Do the synths of the Institute praise "Father" because they are programmed to or because they want to? This is not known.
He does seem to tolerate dissent among the Directorate though does not extend any mercy to sabotage or treason. It is important to observe that no one in the Institute seems to have a fanatical hatred of any group, or be existentially opposed to anyone who does not interfere. They see synths as property and are very good at rationalizing this idea, but because of this they are blind to things beyond their black and white perspective. The synth at Libertalia, for example, was not always a psychopathic killer from the moment he was freed. His terminal shows he was once a dedicated Minuteman turned brigand by the threat of starvation, who repeatedly tried to do the right thing before giving up on it and accepting his identity as a raider - a very humanlike transformation. Yet Shaun was not wrong in stating that presently, the Commonwealth needed to be protected from this rogue synth.
Extremism Rating: 5
Violence Rating: 6
Authoritarian Rating: 7
Deception Rating: 7
The Brotherhood of Steel
Is the Brotherhood of Steel genocidal? If ghouls, super mutants, and synths are persons, they certainly are. But that is a judgment a person must make. The word genocide can certainly be used unfairly. An extreme animal rights' activist may call meat production genocide and point to the relative intelligence of domesticated animals. The elephant in the room that the Brotherhood of Steel wants to end a whole lot of lives also has to be looked at in the context of the greater good. "War never changes", and all major and important wars have involved mass destruction and deaths of people - which those who wage the war would say is for the sake of protecting humanity as a whole.
The Brotherhood is not particularly merciful toward the people of the Commonwealth though, extorting food from local farmers with no apparent ethical questioning. They are arguably the most dedicated and the most fanatical of any of the three factions. Yet they can see in gray rather than black and white if they squint hard enough. Maxson can be persuaded into sparing Danse, Haylen chose loyalty to her mentor over ideology, and Danse gains some empathy for a synth's right to live by the end.
There is a great respect for loyalty and order within the Brotherhood of Steel. Their troops are dedicated but they do not see them as expendable property as the Institute does their synths. For what its worth, the Brotherhood really never lies. They tell you up front who they are and what they've come to do with some exceptions.
Extremism Rating: 9
Violence Rating: 9
Authoritarian Rating: 7
Deception Rating: 2
I welcome any and all thoughts, criticisms, and commentary!