So I plan on making a companion mod in New Vegas and wondered what made NV companions more interesting than their Fallout 3/4 counterparts. They both had dialogue full of exposition and backstory but I can’t put my finger why the New Vegas companions have more depth

Simple. Natural evolution of the character.

In fallout 3, companions basically reveal their entire life story the moment you meet them (if they have one, like Fawkes) and then they can never really be spoke to again. In Fallout 4's case, their story comes in the form of small dialogue snippets that come in intervals, that are unlocked by gaining approval. While it's a step up from 3, it still feels unnatural as there is no real prompting, ie the player questioning them as they travel.

Dialogue trees in FNV as a whole were far more expansive. You could frequently ask your companions questions about themselves and their lives, including questions which would only appear after the player learns of certain events (like Boone and Bitter Springs). While each companion had triggers for their approval, which unlocked more questions, these were more specific than picking locks and hacking terminals, usually relating to their own stories, (like arcade and the crashed Vertibird) and the new dialogue options felt more like followups to questions the player had already asked as opposed to the NPC unpacking their life on you piece by piece. It showed character when someone like Boone reacts to the players choice to kill or save the captured soldiers in Nelson, and he explains that he frequently had to kill such men himself, and deeply regrets it, or when the regularly guarded Raul questions his own self worth after seeing how other old timers can remain so useful to their community when he feels worthless.

Tldr: The point is, FNVs companions are tailor made for their world and have specific tie ins to story and locations that lack from Fallout 3/4. It's something that needs to be present to make the character a part of that setting.

Ohh okay it makes more sense now haha. Thanks a ton! I knew it had something to do with Nv’s expansive dialogue but I completely forgot the difference in how backstories were revealed in both games. Thanks again guys!

If you want depth, and character development, you have to plan ahead for the long-game. You want a decent idea of them up front, some points of interest, but you want more revealed as you go, and most importantly you want some changes to happen to them as they progress so that they're not entirely the same person by the end. It takes a while to write out a good character arc, and it won't be easy, considering this one has to shape itself over the course of random gameplay with another character who is acting as the lead protagonist and therefore requires the companion as a "support character" to their own arc.