I'm going to include the overall package when comparing both games and will say Fallout 3 was the better game.
At least from the standpoint of the overall experience.
Yeah, the story was crap, the characters were uninteresting and the side content was a bit useless (outside of a few quests like the one where you enslave people, the one with the android and the one where you shoot the heads off people) but at least the game worked fairly well as an exploration RPG.
I mean, there were skills, you had perks, levelling up felt somewhat rewarding, the Vaults were somewhat interesting and some of the other Locations were also pretty good.
Simply put, the game needed more work done to it to really be a good game.
Lets look at the DLC, I think it's safe to assume that at least one DLC is very good (Point Lookout) while The Pitt was also decent.
I can safely say that at least 2/5 DLCs was acceptable (while Broken Steel carried on past the ending and Operation Anchorage is passable).
The game is just kind of decent.
Fallout 4 on the other hand, feels really bland.
Role-Playing has completely gone, the characters feel even more uninteresting (some of the Companions are an improvement through), the designs look ugly, the dialogue wheel is so cancerous, it gave our son cancer.
The game is just such a weird thing.
The Locations aren't as interesting as even F3 (and for the record, while I like some of the Locations in F3, they are still below games like F1 &2).
The main story, while it had more potential, was just a rehash of F3's first act with a bit of New Vegas thrown in for good measure.
And then we get onto the DLC, I actually despise the DLC in F4.
For one thing, the Settlement mode doesn't work as it should, it's a broken mess.
You know what sucks, having to build fucking settlements from the ground-up in first person.
You know a game which does the building mechanics better? The Sims.
Why? Because the Sims is fucking isometric. Something which Bethesda would hate to do because it'll remind people of a good game.
So yes, Fallout 3 is better than Fallout 4. The only good things about F4 are the combat, and how weighty the PA feels. That's it.
And even then, they got help from ID Software on how to do Combat properly.