I would be surprised if Bethesda didn't at least consider some of the finer points of New Vegas - that's what I found interesting about Obsidian making a spin-off to the game, was to bring a bit of a different perspective to the games. If you don't at least take a look at what another company does with it's take on your franchise (after you've hired them to do so,) then that seems like a huge wasted opportunity. I just can't imagine them not at least seeing what elements they personally liked about the game and thinking of how it would fit into the next installment.
There's a couple of more minor things that I really enjoyed in New Vegas. For one, I found it kind of a subtle addition, but all the achievement perks and incremental collection sidequests (kill so many creatures, pick so many locks, etc) I felt actually brought a lot to the table. Going back and playing through Fallout 3 I found I really missed that feeling that just about everything I was doing was progressing me in some manner, albeit a very small amount at a time.
Certainly the forethought and planning of the major settlements and their niche in the local politics and ecology would be worth considering if I were making a follow-up game.
Also what I felt was a really nice little touch was the specific slang and dialects you'd find among various NPCs. Vault-Dwellers used relevant terms and their jargon fed into the background - likewise with a lot of other types of characters (the Vegas gangs had their dialect separate from the Raiders you'd encounter, for example - you could tell a line was from a Caesar's Legion versus an NCR soldier.
I feel like Bethesda certainly liked the expanded crafting in New Vegas, from what we've seen of Fallout 4. Maybe that's something they would have done all along, but I think there's an argument to be made that was an influence from New Vegas.
I liked the idea of hardcoe Mode (and always played with it on,) but some things I liked and others I didn't feel worked particularly well:
The delayed healing I found impactful on my playstyle - no longer was I just keeping one finger near my Stimpak hotkey, when I got into trouble I'd have to withdraw and find enough cover to give me time to heal up. I think it really changed the pacing of a lot of fights, and needing specific items to heal crippled limbs meant that I was no longer just removing those statuses as soon as they came up. I found myself actually having to deal with a crippled limb more often with hardcoe Mode on than I did while playing Fallout 3, where it was rarely a consideration for me.
All the hunger, thirst, and sleep meters I found interesting in principle, but they become at best an annoyance to me personally. It was never much effort to just keep a well-stocked fridge, I found - more than anything it just meant I was spending more time managing my inventory. I rarely ran out of these items anyway, so it became more about having to go back to resupply and spending time in inventory menus.
I tend to think of the sort of gameplay you want to encourage when you introduce a mechanic. On paper I see the purpose of these survival elements as encouraging more scavenging in the game, which I feel is a good fit for a post-apocalyptic roleplaying game - you're dealing with a harsh world where you loot every single body and open every box to find rare resources you need to survive. I liked the idea of making food more important but honestly I think you'd end up with the same sort of actual gameplay if you just made Stimpaks rarer, more valuable, and more potent.
If Stims were the sort of thing you stockpiled for emergency situations and food and water were reserved for "topping off" your health between battles then you're already eating and drinking more than enough to fill whatever meters there are.
Really, I think I'd be just fine if hardcoe Mode did away with the survival meters altogether. Really, I'd probably just as soon see something where you could "take a load off" after a battle or finding somewhere quiet to sit down and top up with food and water. I think just seeing my character sitting down at a table and grabbing something to eat with some special animations would be more interesting and immersive to me while still encouraging the same player behaviors (and more elegantly, I think.)