honestly i had to think hard about it. but i really do think the institute provides less to the people of the common wealth altogether and in my opinion has a far more disastrous future if left alive.
BoS: are racist, yes, very militaristic but look at the current state of the common wealth. super mutants running ravage, feral s in every building, raiders roaming the hills. i think a little bit of cleansing is bit necessary for the sake of the commonwealth civilians.
The institute: Yes, after meeting them they have good intentions, yet what they are scientists without boundary. what was vault-tec? the same thing. what if their new hyper intelligent model synths rise up against their human masters? then the institute fades to synth, they can mass produce themselves and eradicate the human race. because if EVERYTHING about a synth is human, includeing thought process, then so is greed and bigotry. why add another problem to the wasteland?
Railroad: i dunno, i killed them all on accident. my bad, mis-interpretation, couldn't load a save so the knowledge i have of them dies with it.