Bethesda can do amazing writing when it wants to, just as it can also turn in Journeymen work when they're not being pushed to. However, one thing I do appreciate in this game is it really does have a bunch of stuff tying into the main quests from side-quests and companions. This is a thread to talk about what you LIKED in the game story-telling wise and why.
1. Companions all reflect your emotional journey: All of the Companions have some tragic event or signature moment in their pasts which has caused them to reinvent themselves or they're struggling to define themselves when they can't define themselves by what they used to be.
Curie wants to become human
Preston has no purpose without being a Minuteman
Piper reinvented herself as a newspaper woman but lost all of her friends because of it
MacCready is an ex-Gunner who lost his wife and is looking to save his child
Codsworth can finally recover his lost master but his lost master isn't the same person he was before
Strong wants to find the Milk of Human Kindness
Nick Valentine is stuck trying to be a Synth with his own identity when his identity is inherited from a dead man with values from a Pre-War world
Cait is suicidal because of her past abuse and guilt
2. The Railroad and the Sunshine Co-Op: Professor Goodfeels is a robot which has been reprogrammed by do-gooders who don't realize he's a nonsentient robot. I.e. a potential parody of the Railroad and their views.
3. The Submarine Mission is about the pointlessness of war and hollowness of victory: The Yanghtzee mission is about a Pre-War soldier and a communist Captain working together to put aside the past even though the latter murdered the former's home. Or, it's about repeating that war, 200 years latter and getting revenge. If you kill him, The USA "wins." Congratulations.
4. Kellog is the Sole Survivor and the Sole Survivor is Kellog: This is a bit obvious but Kellog is the Sole Survivor if they went an Evil Karma Path and sided with the Institute. The Institute accepts you because, essentially, they think you're Kellog. Kellog lost his spouse and child and it made him a hollow shell of a man who killed everything in his way until he sided with a faction for the comforts.
5. Revenge is impossible and so is regaining your past life: The people you've been chasing who committed all of the Institute's horrible atrocities like Vault 111 have been dead for decades. Shaun is all grown up and dying. In short, trying to recapture the past is doomed to failure.
6. Subverting the whole Arthurian myth with Arthur Maxson: He's a boy king and conqueror but very clearly NOT what Elder Lyons or players from Fallout 3 expected.
7. Paladin Danse: Paladin Danse being from Rivet City is a delightful bit of foreshadowing since that's where the Railroad was dumping their high-quality synths from the beginning.
8. War Never Changes: For once, the motto of the game isn't just a cool thing to say ala Samuel Jackson and his parable in Pulp Fiction. There's actually a theme of two sides, flawed and good at once, being unable to prevent themselves from going to a war which pointlessly results in a nuclear annihilation that leaves the Survivor with the blood of innocents on their hands.
9. The Questline means you'll get to know every faction: You can't just shrug them off as the bad guys. You have to get to know all of them at least to some extent. That way, you're betraying someone.