After Fallout 2, Interplay decided to drag their franchise through the mud and vandalize the cult classics they had created by releasing an outsourced mess with Fallout Tactics in 2001, cancelling Black Isle's Van Buren (the original Fallout 3) and ultimately releasing a horrible console spin-off instead. The latter which was done in-house, without any care for their own intellectual property; it was a complete disaster.
It was at this state in 2004, with the Fallout IP devalued to the price of peanuts, that Bethesda saw the opportunity to step in and buy the rights to release their own Fallout 3. Van Buren was no more, though, and Bethesda had to start from scratch, albeit with a lot of help from their already developed and tested Gamebryo engine used in TES IV: Oblivion. However, the Van Buren tale was not yet completed: Chris Avellone and Feargus Urquhart had left Interplay after Black Isle's dissolution and went on to found Obsidian Entertainment, which ended up developing New Vegas in 2010, but I'm jumping ahead.
Bethesda ended up releasing Fallout 3 in 2008, an open-world first-person sandbox, much like their own previous games but unlike any of the original CRPGs from Black Isle. Besides the disapproval of the a few original fans, Fallout 3 was very well received and tapped into the huge mainstream console market audience that Bethesda had recently acquired with Oblivion. It was a huge hit sales-wise, dwarfing the niche CRPGs that came before in comparison. That said, public opinion has been very much swayed over the years, especially after the release of Fallout: New Vegas, which had much more in common with the franchise's roots than Bethesda's take on it.
This shift in public opinion is also a consequence of the fact that more people were retroactively introduced to the first and second games after the franchise's surge in popularity. I include myself in that camp as well -- replaying Fallout 3 recently made me realize how my positive memories of it were mostly due to it being the first Fallout game I had played. In retrospect there's a lot to criticize here, but I still think that the core of it, and what Bethesda was able to pull off by resurrecting a dead franchise, is very impressive.
Adapting an isometric turn-based RPG into a real-time first-person shooter without sacrificing anything in the process is impossible, so Bethesda cut their losses and focused on what was the strongest aspect of the franchise: the unique worldbuilding and visual design. They didn't sacrifice everything else though, the unique RPG system created by Tim Cain and Chris Taylor was still used here, although primarily as flavor rather than anything else. Skills, Perks and the S.P.E.C.I.A.L. attribute system all made a comeback. Much of the system was rebalanced and reworked for real-time combat. Aimed shots are now the V.A.T.S system. Radiation seems more prevalent in the moment-to-moment gameplay, but it's overall easier to deal with and that permeates in every aspect of the game's design. It's a ridiculously easy game with pretty much no challenge from start to finish. Consumables, ammo and almost every item are plentiful in this supposedly scarce wasteland. Character builds seem mostly redundant and you'll end up good at everything even by the mid-game. This lack of difficulty and build identity is what is most lacking mechanically in an otherwise great system adaptation.
The good thing though, is that the whole visual language of Fallout's universe was very well adapted. The overall themes and quirks that make this post-apocalyptic retrofuture so interesting were kept mostly intact. Unlike the horrible last attempt from Interplay, Bethesda's Fallout 3 understood the language of Fallout and what made it so good. The wasteland is now a character in and of itself and was expertly translated into a 3D open world like only Bethesda could do at the time. The incredible sandbox exploration gameplay loop that Bethesda had pretty much perfected at this point worked so well here that you'd think the franchise was made for it from the start.
The aspects of which I think Bethesda really failed in translating into a more modern era was the writing/narrative and roleplaying part. The setting is now Washington D.C., a whole new side of the country where they could go ahead and tell new fresh stories. Unfortunately, they didn't really grab this opportunity and instead decided to tell us the same stories and tackle the same concepts we got before, but in a lower quality: the Enclave is back without much reason or purpose; the Brotherhood is here and very much less interesting than before; the people need fresh water and you need to retrieve the G.E.C.K. All ideas taken directly from the first two games, distilled to their most superficial level and jumbled together here.
It also doesn't help that the dialogue is completely dull and the choices are basically non-existent. The choices that do exist are all binary or without payoff. Villainy is treated in the most cartoonish way possible. There's no reason to roleplay as an evil character since the rewards are not skewed towards it at all and there aren't any in-character motivation to do so except to end the conversation quicker and start a gunfight.
With all that said, the most memorable stories will come from the emergent gameplay. There are a few interesting crafted stories that are worth experiencing, though. Most of them are told through environmental storytelling, like when you're exploring the five other vaults and figuring out their fates. Some interesting and memorable quests are: Agatha's violin, Reilly's Rangers, the Oasis (has an interesting cameo from the originals) and Moira's Guide.
Finally, I'd still say that Fallout 3 was an impressive achievement from Bethesda and even if it fails narratively, it was still one of the best possible outcomes for a near-dead franchise. It modernized and laid groundwork for the subsequent titles, and its success created the perfect opportunity for the Van Buren project to be continued in the hands of the legacy developers at Obsidian Entertainment with Fallout New Vegas, at least in spirit. New Vegas ended up surpassing its predecessor in a variety of ways, being considered the "true" Fallout 3 by a lot of fans, but its older, uglier cousin is still worth a playthrough.