I would consider New Vegas as the only playable Fallout game under Bethesda. 3,4,76 just ain't Fallout. Or much of an RPG, for that matter.
I don't know if you played the previous Fallout titles (1+2, most notably), but if you did, then you would know that New Vegas was more like a return to sources, literally so even: The Devs were also the people who made Fallout 1+2 in the first place. They mostly just put things from those games back in that Bethesda cut out in 3.
I don't care if they're like the first two games in the slightest, I only care if I like playing them. Doesn't matter to me if they mimic old RPGs, either. I don't go into a game thinking, "if this isn't like earlier games then I refuse to enjoy it." I have no idea why you are unable to play Fallout 3 or Fallout 4 because I had a blast with both, just as I did with New Vegas.
I have 800+ hours in New Vegas but I'm not going to deny that it was a flawed game, especially with regards to "RPG" elements like karma and the terrible faction system. Thankfully, there were a multitude of mods to make them less annoying and nonsensical. I went back and played New Vegas after I beat Fallout 4, which did a lot to remove my nostalgia glasses.
Hopefully Obsidian has learned some lessons or I'm going to wait and see if mods come to the rescue again.
Apart from the bugs, horrid tech and being so dumbed down I can hardly qualify them as RPG anymore. Especially 4 is more a looter shooter than a real RPG anymore. But hey, the dumbing down helped with selling the franchise to casuals, so the sales exploded.
Since I went through most of the world-building with 1,2, Brotherhood of Steel and Tactics, that part wasn't new to me. In fact, the changes they made was more eerie to me most of the time. Like that constant 50's soundtrack (1+2 had just the wind howling and sometimes ticking of Geiger counters outside of towns. 50's music was only used in intro videos). Power Armor only really was a thing only for the endgame (unless you made a very specific run in Fallout 2, and even that one only works through excessive save scumming), same with the most powerful weapons. What's left was the gameplay and that was pretty much boring to me. Like I said, to me, they're pretty much the original looter shooters. New Vegas fixed the game, not broke it, as far as I'm concerned, it made Fallout an RPG again.
As for Obsidian having learned their lesson, have a look at Wasteland 2, and judge.