Offtopic but speaking about your example: Curiously enough, a similar situation happened to me but with F3 and NV. Before I got a 7th gen console (or a capable PC) and being a big classic Fallout fan I could only dream of playing F3. When I finally got it I enjoyed it a lot (with some exceptions) yet when I got NV it was like a revelation. Same engine and basically the same gameplay yet the changes in NV made F3 basically "obsolete" for me. I haven't played it since (though maybe I should) just cause I'd rather play NV again.
All that being said, I have yet to play F4 due to the criticisms I've heard on the gameplay and the story. As someone who LOVED NV, do you think it's possible I could like F4? Specifically the story and if the story isn't good, can it still be enjoyed regardless?
Depends on your mindset. If you go in with the preconception that "Bethesda sucks, I'm gonna hate this because it's not exactly like New Vegas" like some of the vocal "old school RPG" people then, no, you're not going to like it. The Fallout message boards were full of people who hated Fallout 4 before it even released and were trying to convince everyone else to follow their lead.
Assuming you're not that type, then you should like it regardless since it's the same template. I really can't understand someone liking one but not the other. How much you like it depends.
If you love exploring open worlds filled with lore and interesting encounters, like me, then Fallout 4 is incredible. In that regard, you can't really compare the two games because of the massive content differential. In NV, you can see pretty much everything in a few hundred hours. In F4, it would take you THOUSANDS of hours to see everything. Plus, F4 has all these details about the people who lived and died before you ever showed up that I absolutely loved. I think of it as "environmental storytelling."
Pure gameplay, again, F4 is a massive improvement. Same with QoL features. SO MUCH more fun to fight a gang of Raiders or Super Mutants and there is always something around you calling for your attention.
As for the story and main quest, it's kind of funny, but F4 and NV are really opposites. New Vegas starts out with this fantastic premise where you're shot in the head, left for dead, and then go out seeking revenge. Total cliche but it's obviously supposed to be a nod to the classic western. Then there is a turning point where things go straight downhill--there are goofy Roman soldiers, laughable climactic battles, shoe-horned events that come out of nowhere, and the eye-rolling revelation that it all revolves around the worn-out "hidden cache of super-weapons" plot. I will never not hate how it devolved near the end.
On the other hand, Fallout 4 starts out with a prebuilt character history (annoying--I always use a mod to change that now) and the lame motive of rescuing your kidnapped child. Now, if this were a book, F4's premiss would be more interesting, but this is a GAME, so it just ends up feeling like baggage that you don't actually care about. However, once you get that out of the way, F4's story of an inevitable confrontation between three different groups who can never see eye-to-eye actually starts to pay off. The endings are FAR more fun to play through and can vary greatly depending on which side you choose, with some really tough final battles.
Either way, the 'story' in both games is just fluff designed to move you from one event to another. Neither are very good beyond that.
That being said, if you are one of the "role-playing has to mimic pen & paper conventions" types and you want your game stuffed with "RPG systems" where the developers set everything up for you like a DM then you'll probably like New Vegas a lot more. I'm more of the free-form type, I prefer to make my own rules and use my own imagination to govern my character, so F4's settlement building system was a god-send. FOR ME, it was the best role-playing game I've ever played--I built settlements the way I WANTED and played as much in my own imagination as in the game. For instance, I did a dark play-through where I cast the Minutemen as fanatics and placed things like torture rooms, holding pens, and execution pits in their home settlement (using mods to add more flavor).
Then again, Fallout 4 does have a Survival Mode that a lot of old-school RPG gamers love. You have to sleep, eat food and drink water, fight off disease, and deal with a lot more of the details of surviving. No quicksaves or fast travel, either. I found it tedious but it's very popular.
In short, I think if someone hates one and loves the other then it's probably because they're a sucker for their own propaganda. Fundamentally, they're far more alike than they are different.