Honestly, the writing is worse than D3. D3 is just a generic silly cartoon fantasy. D4 tries to pretend be look dark and edgy, but it's actually filled with bunch of stupid and illogical plot twists.
While the writing in D4 is pretty bad especially for a few of the characters (lorath and the girl who's name I forgot) I still find it much better than D3. Not a high bar to reach but at least D4 was somewhat interesting and had *some* interesting plot hooks that I remember positively like the guy being absorbed into the tree in act 2 (?), the tree of whispers and the whole sequence in the swamp, Inarius being a genuine asshole, Mephisto (even though that "plot twist" was so visible). I also think Lilith's character was somewhat interesting though I've seen this is a pretty hot take.
D3 on the other hand, the only "memorable" moments are because of how horrible the writing was. Deckard Cain and Leah are the obvious ones alongside whatever the fuck Belial was (Lord of lies my ass). I could write a fucking essay on how bad and uninteresting the whole nephalem plotline was.
The one thing that I remember from d3 positively is the cutscene with tyrael vs imperius. If the game tried to be less serious in the story department (and no, unicorn island doesn't count) and had more action shlock like that I would've liked the game better.