This is something I'm struggling with as I haven't finished the game after 86 hours (I don't care about spoilers).
Let's take them one by one:
The Minute Men - A wasteland militia that's dead set on being the "peoples militia" and generally wants to ensure the cooperation of all settlers in the Commonwealth.
The way I see it, they're the scrappy underdogs who'll eventually end up like the NCR as soon as they establish a government.
There's a lot of information missing, because you're the general and governor rolled up in one. If you could recruit or promote people to mayor, then you'd get a better idea of what'd happen in the future.
The Brotherhood of Steel - A militant BOS chapter led by General Maxson, a young zealot guided by principle and adherence to the belief that advanced technology should only be used by them.
Since this is the same chapter as in Fo3 (ugggghhh), they're also interested in helping the average settler out there. However, they will only do so if it coincides with their goals (appropriating tech and killing dangerous beings like mutants).
Despite their arrogance, they stick to their principles. While they view the populace as common peasants (they're not wrong though), this chapter has a history of helping them.
The Railroad- Underground liberators that help synthetic humans/androids escape and stay hidden away from the institute.
Their objective is to help synths as if they were sentient and free-thinking individuals and seek to free them.
I've always hated the whole synth/railroad lore ever since I heard about it in Fo3, so I'm obviously biased on this...
So here are my issues with the railroad - they have so many resources that they can afford to help very specific individuals of which there are maybe a hundred of, at max. That's it, there's nothing more to it.
Why aren't these people helping other people alongside the synths? Why aren't they out there dealing with raiders, feral ghouls and super mutants?
They're effectively just helping synths into a horrible world, without doing more about it. I can't think of the railroad as anything else but a product of lazy, bad writing. Even b-movie productions have a reason for a faction or character to exist.
The Institute - Researchers and scientists who grew up below CIT who use robots/androids to further their goals above ground.
Basically they're know-it-all scientists who haven't experienced the world above and have goals that are beyond the mere survival of the people above.
The institute is another poorly written faction, if for no other reason than the fact that they somehow managed to build a super high tech city below Boston without going above ground to get materials or machines.
These basemant nerds are generally unsympathetic and while their work is extremely important in general for human kind, it's unrelatable to the world above.
It is stated by them that synths are just machines, effectively making the railroad a useless faction. Since we don't have any other information to relate this to, there's no reason to believe that they're lying or wrong.
It might be that synths are sentient enough to merit being "people", but then the Institute would've had to face this fact a long time ago.
There's little other to them than their self-preservation and due to the lack of dialogue options and any real lore to dig up, they don't really have anything going for them.
----------
So in the end you have two choices of "good" guys, the Minute Men or the Brotherhood of steel. The first is another NCR waiting to happen and the latter is militant civilization through superior firepower.
My assumption lies in the the fact that the Institute says synths aren't sentient. If they are (boo) then the railroad is likely the "real" good ending.
All in all you can chalk the storyline up to piss poor writing and not bother with it any further than seeing the different endings for your entertainment.