They are both just as dumb and bad as eachother but Fallout 4 at least gets points for originality with the Institute/Minutemen/Railroad, however poorly executed.
Fallout 3 on the other hand decides to rehash every plot beat and every major faction from Fallout 1&2 on the opposite coast where it makes no sense for them to be because Bethesda wanted to milk that Fallout iconography. 3 is a soft reboot made with all of those things included because Bethesda never expected anyone to give a shit about yucky old 2D isometric games once their latest and greatest iteration of the series came out.
>Hey, remember the BoS? How they were barely present during Fallout 2 and small scale compared to the current events? Well here, have them back with their numbers multiplied by 10 because we needed a 'good' faction.
>Hey, remember the Enclave? How they were totally annihilated during Fallout 2 and only small contingents of them remain? Well here, have them back with their numbers multiplied by 10 because we needed a 'bad' faction.
>Remember Super Mutants? Those guys who were mutated by FEV from the top secret West Tek and Mariposa facilities? They were lead by the Master and his Lieutenant in Fallout 1. Who are they lead by in 3 and what are their motivations for kidnapping people and taking them to turn them into super mutants in their vault which inexplicably also has FEV? Nobody. The only smart super mutant around is locked in a cell because he's different. There is no intelligent mind leading them, these cannibalistic barbarian ogre people kidnap people and turn them into more mutants because they just do ok cool. We needed an ogre bullet sponge faction. Did I mention that a town full of children with one kid with a gun is able to hold off a horde of these things?
>Remember Radscorpions and Deathclaws? You know, from Fallout! Have them on the east coast because that makes sense.
>Remember bottle caps? That currency that was backed by the water merchants of the hub in Fallout and phased out by the time of Fallout 2? Well guess what, we have bottle caps on the east coast too and they're backed by literally nothing.
>Remember when the vault needed purified drinking water in Fallout? Well that's the basis of our whole plot, the wasteland needs purified drinking water!
>Remember when the overseer said you were a hero and you had to leave, well guess what, you're that here too!
>Remember the GECK? You know, that macguffin from Fallout 2. Go find a GECK to save the wasteland!
>Remember Harold? That old mutie that settled down in Gecko? Well he's inexplicably walked across the continent and turned into a tree for our game.
It's literally the most lazy rehashed garbage ever put into a video game, Fallout 4 isn't great but at least they put a pen to paper at some point during its storyboarding unlike 3 which was probably just copypasted from the synopses for Fallout 1 & 2 with some words changed.
Also Fallout 3's core gameplay is fucking dire and 4 improves on it so much it's unreal. There is literally no reason and never will be a reason to play 3 over 4 if you're looking for dumb low IQ looter shooter. If you're looking for a good Fallout game then 3 is the absolute bottom of the barrel along with Brotherhood of Steel, too. If for some reason you like Fallout 3's gameplay then New Vegas does it better anyway with iron sights, weapon mods, ammo types, actual unique weapons and armor, and just so happens to also be the best attempt at a Fallout game in the modern 3D era. I don't know why you would want to play 3 with its dumbed down RPG systems and shit combat just because the RPG systems are less dumbed down than 4. If you wanted a good RPG why the hell would you play 3 to begin with. Fallout 3 is a painfully boring game where you can get 100 in every skill before level 30 but everything level scales to you so you're shooting bullet sponges for the last third of it.
3 serves no purpose. It is a game for nobody. It doesn't do anything better than any other given game in its own series. The only thing stopping it from being absolutely irredeemable shit is that its existence let New Vegas exist.