1. Stories/dialogs/ aka all things writings related.
Eh, both are stupid, but Fallout 4 tries to be serious and therefore fails worse - Like trying to pretend the Institute believe in literally anything - Game wants to be New Vegas, but you know, New Vegas let you ask Caesar actual questions, it's not just "We're good for humanity because we say so, just don't ask why we're making Synths or Supermutants or synthetic apes or doing literaly anything we do"
2. Art direction: blue tinted saturated urban ruins vs full color sharp contrasted plastic feel.
Fallout 3 kinda has the gothic look with the big heads going on. I think it's world is extremely colorless - Green tint aside, everything is just pure grey - Fallout 1 had limited colours but it still made it's world more appealing to look at than just, depressing grey everywhere.
But Fallout 4's world is just, the art-style is completely different, everything is way too colourful - It looks like a cartoon world, I don't like that either.
3. Quests: number, quality
Fallout 3 wins this category and it's not even close - At least it had quests with branching paths and choices and skill checks.
Fallout 4 is 90% "Another settlement needs your help" - Even major quests put you in corridor shooting dungeons, or have mandatory combat, and there's not a single way you can use skills to solve problems in a unique way beyond speech.
4. Memorable NPC: Piper versus Sarah Lyon? or else?
See, this is a matter of complete personal bias - But Piper sounds like a millenial to me. IDK how to explain it, she just has that vibe. IDK that alone kinda means she annoys me as a character.
The only Fallout 4 companion who doesn't either have no personality, or who I don't find personally annoying is Cait - She's the only one I can tolerate having in my party for more than 5 minutes.