I guess in the end, my feelings on the matter aren't that it is a difficult choice, but there are no good choices . . . by this I don't mean "there are no choices without regrettable sacrifices", but that literally all endings are far too catastrophic than they are good. In my opinion, Minutemen being put to the side for a moment, all endings are BAD endings, because I feel that it would be better to indefinitely leave them unresolved.
Brotherhood
I'm a big fan of the Brotherhood in general, because one of my primary goals in the Fallout universe is seeing a concrete step towards recovering from the Apocalypse, in the form of technology acquisition, research, and structure/stability. I believe that the Brotherhood is a fantastic example of this, and despite their (often variable) fanaticism in many regards, they seem to offer this.
However, I consider the wholesale destruction of the Institute to be a tremendously foolish decision. That was a technological masterpiece; Maxson's comments that it was technology gone wrong are only correct insofar that it this technology is being held by people who are (IMO) abusing it. That research and infrastructure could be requisitioned and re-purposed towards the Brotherhood's own ends . . . there is nothing "evil" about a teleporter, or a clean, air conditioned housing complex. The Institute was an asset to the Brotherhood's core tenants, not an object of evil to be destroyed.
Meanwhile, killing the Railroad was such a forced and unrealistic decision that I literally cannot blame the Brotherhood for it; it feels like game design meddling. This was something they deliberately put in the game to make you feel bad about the Brotherhood; not just because you did it, but that they made you do it with your own hands like that. I'll point out that there was literally no speech option out of this . . . Kells informs you of your next mission and the Railroad is IMMEDIATELY hostile, you cannot refuse this, you can't even betray the Brotherhood to re-side with the Railroad. That's not a fault of the Brotherhood, that's weak game design.
Finally, killing all synths is, like the Institute, a stupid decision. This whole "they are abominations" crap sounds far too pseudo-religious for my tastes, and personally, I found it to be out of character for the Brotherhood to get this way . . . not against, but "must be wiped out at all costs, nothing more to say". It doesn't help that there are no less than four synth companions at your disposal, so this is like murdering a fourth of your close friends.
Institute
The Institute had a lot of promise for me . . . it seemed like they were offering something great, a huge step forward in advancing the recovery of civilization. Ideally, I'd support this, but it seems like they were literally going about it in the most stupid way.
You see in their research that they were studying human augmentation, and had even succeeded with the 100+ year old Kellogg, but for some reason, decided to say screw it and went with Synths instead. But even that doesn't make sense . . . one of their own scientists said to me "How can synths be the future of humanity if they aren't human?" Since the Institute seems 100% convinced, without a doubt, that synths cannot be considered or treated as independent beings, where is the end goal here? To make hyper advanced robots that are slaves of humanity, even while humanity itself lives no longer than it ever did? What's the point? Some of their propagandistic speech even indicates that they have really no interest in ever returning to the surface, so I can't even figure out what they want to do. I can only deduce that their end goal is making perfect synths and then living in their personal vault for all eternity, and that's really stupid.
So with that said, their insistence on destroying the Brotherhood (one of the organizations that might actually HELP the Wasteland at some point) and the Railroad, as if they are a cult of evil idiots is really weaksauce. You end up siding with an organization with all of the means and motive to completely resolve the apocalypse, but instead they have decided not to.
It doesn't help that, again, they want to enslave all synths, which again amounts to 4 of your companions (though I suppose one of them is already under Institute control). What if they meet my Curie? Or decide they changed their mind about Nick Valentine? But with the writing in this game, I'm sure that I would have no options to say no, there would be no changing my mind or betraying them, it would just be "bye bye companions" without a care in the world.
Railroad
I'll give them this . . . their hearts are in the right place. And that's pretty much all I'll give them. They've got some infrastructure and resources, they aren't incompetent, but their end goal is "liberate synths", and since their end play is "destroy Institute", they've eliminated the source of synths as well. Once all the synths are liberated, they have no further function as an organization and will dissolve . . . resulting in nothing. You've just sided with no organization, at the expense of two of the most important factions. Either the BoS OR the Institute could save thousands of lives here, in the right context, but you can instead destroy them entirely for the sake of an ethical stance that will cease to be relevant after the fact.
Let me tell you something Desdemona; you know what ELSE is unacceptable? 500 raiders running around the Commonwealth, murdering people by the hundreds. Super mutants, ghouls, deathclaws, STARVATION. These are ever present threats and I don't see you doing a damn thing about them, nor do you seem interested or to even care. I do care about synths; I believe they warrant freedom and autonomy. But I'm not going to blow up the wasteland's two greatest hopes for a relatively small scale ethical dilemma. If I had to choose between freeing a few hundred synths, or siding with a faction which will bring a measure of stability and safety to the region as a WHOLE, perhaps even further with enough time, I'm picking the latter.
Railroad is an ethical stance, its not a real option, and they don't impress me enough to make me think they are worth supporting, despite their good nature.
So yeah, that's my problem with the choices in the game . . . each one results in far too much collateral damage for me to justify the choice being made.