I got around to thinking about what it means to join one of the four factions of the Commonwealth. It occurred to me that each one offers a different moral alignment ranging from good to evil and everything in between. Below is just my take, I'd be interested to hear what others think of them.
Railroad
They represent the "Good" moral alignment: total selflessness. They don't want power, they just want everyone to be free no matter the sacrifices required to do so, even if those "people" aren't even really people.
Brotherhood of Steel
The Brotherhood, to me, represent neutral/ambiguous morality in this chapter of the U.S. They believe the way to achieve total peace and progression of the human race is to take absolute power from the common man, so it can be put to better use and he can't hurt himself with it. Sort of like tyrants with a good end-game in mind, or in their minds at least. They want to eradicate abominations of nature such as super mutants, ghouls and synths and anyone involved in the making of them. The Brotherhood have no less qualms about gutting a fleeing, unarmed scientist than an Institute Courser. They are the flying, looming battlestation with every cannon and energy rifle on full display that blasts through its speakers "we just want to help".
Institute
Evil. They want power, and like the Brotherhood they don't want to share it, but unlike them they aren't concerned with anyone's freedom or the welfare of the common man... they want to reshape the world in their image, by force, by any means necessary. They don't care who they have to hurt and they think themselves above the common wastelander, they've even created synthetic humans to replace them. They want efficiency and perfect, impurity isn't to be tolerated, and they put their mission to reshape the future above absolutely anything else, regardless of the moral leaps they have to take.
Minutemen
And then there's the Minutemen who I'd say represent realistic human morality: they don't have unbelievable technology, or power, or an extremely narrow and well defined cause they're willing to slaughter armies in the name of even providing they had the resources to do so... they just want to get to a place where the common man can get by. If they need power to do that they'll take it but it's not what they really want, it's a means of reaching a peaceful state. They aren't perfect; they're human, they have prejudices, they can be shortsighted, they fear what they don't understand and lash out, as we all do, and they sure as hell aren't the most technologically advanced, but they take what they've got and make it work for the good of the common man for a better future.