I don't know if anyone already replied by saying the same things I am going to say now,, but there are 4 pages of posts and I don't have the time to read them all (specially with this slow and freezing browser).
In Fallout 2 they grabbed what they had from the first game and mainly expanded it (doesn't means that doing that was a good or bad thing for everything though):
- They expanded the world
- They expanded the size of locations
- They expanded the story
- They went all out with expanding the wacky stuff
- They expanded the weapons
- They expanded the quantity of quests
- They expanded game features (like the "push" button, that allows us to push a NPC in case they lock our character by blocking the way, they also made the "arrow system" which allows us to click an arrow and loot the next body under that one, etc)
- They expanded the way skills are used (added more things where you can use your skills, like dialogues, world objects, quests, etc)
- They expanded perks and traits
- They expanded replayability (due to more options and number of quests and how many ways we can do quests differently)
- Probably other things got expanded that I can't remember from the top of my head but you get what I mean (or I hope you do).
In Fallout 4 they grabbed what they had and mainly diminished or "removed" things from it (again doesn't means that doing that was a good or bad thing for everything though):
- They removed the previous setting and moved to a new shiny brand new one (keeping some references, characters, etc from the old one)
- They removed skills
- They removed "perk" checks (I am talking about Base FO4, not Far Harbour)
- They diminished the dialogue options
- They diminished the ways we can do quests
- They diminished the replayability of the game (because in one go we can do most quests for several factions)
- They removed game ending slides
- They removed (or diminished depending on who you ask) the roleplay factor of the game
- They diminish the amount of weapons
- They removed the weapon and armor durability (except of Power Armor)
- Probably other things got diminished or removed that I can't remember from the top of my head but you get what I mean (or I hope you do).
What Fallout 4 added was voiced PC and a more indepth craft and settlement building.
So I managed to remember 10 things for both games. Of course the games had other things that were changed, added and/or improved (gun fighting, graphics, etc). But for me the most obvious mentality in both game designs were for Fallout 2 expand and improve Fallout, and for fallout 4 remove and diminish Fallout 3 and instead make things more pretty and action-y.