The main story is good. It's on par if not better than all of the previous Fallout's (significantly better than Fo3, for sure). There are some glaring problems, though. Largely, it has to do with the beginning and the overall pacing.
They pushed for sentimentality with the family, but the game opens up and there's no nagging urgency to find your son, even though you're supposed to be the concerned husband/wife. There's some serious dissonance between what is established and what you end up ultimately doing. Witcher 3 made people care for Ciri not because Geralt cared, but because there was expositional segments told through gameplay to establish Ciri as a character, and then there was an entire act of the game spent helping Ciri as Geralt (further establishing a father/daughter motif).
It's funny, Geralt seemed more like a father to Ciri (who isn't even of his blood) vs the Sole Survivor and his relationship to Shaun. Both games started off in roughly the same way: go find X person. It's just that one built up the relationship better than the other.
I feel like the pre-war segment should have been a longer, more in depth view in the sole survivor's life. It would have been a good opportunity to establish the circumstances of Nora/Nate's relationship, and how they ultimately met and had Shaun. Key talking points would ultimately establish whether the SS was a loving husband and father, or an abusive [censored] that was forced into a shotgun marriage.
Furthermore, the decision to axe the NPC spouse (that early) was the wrong thing to do. I saw another opportunity to more or less iron out the relationship between Nate/Nora. How would the two cope with the loss of Shaun? They could work together (either a companion or not - doesn't matter) to find Shaun or go their separate ways (with the NPC spouse appearing at key points of the game). A lot of this early relationship building could have been established based on how your character treated the spouse and the baby in the beginning.