Cycas

The movies present the Strider persona and being a ranger as something false that Aragorn must cast away in order to become the king. He must choose one or the other; he cannot be both, and furthermore, it's as if by being a ranger he is running from his destiny and his responsibility. The movies paint him as a reluctant hero, one who must be convinced by others to take the part he was meant to play. Who is afraid of the responsibility (okay, that kinda is fair, it is a big responsibility, but still) his heritage puts on him, and who isn't sure he wants to claim the throne until towards the end of the movie trilogy.

In the books, Aragorn is much less reluctant. If he ever struggled about whether or not he wants to become a king, he is long since past that. I get the impression that what he really has been waiting for is the right time for traveling to Gondor and making his claim for kingship known; had he attempted it earlier, it's very likely he would have only divided the people of Gondor and caused more harm than good for the people. It's only as the events of LOTR take place that the right time comes, when he knows his presence is needed. I don't remember whether or not it's discussed one way or another in the movies, but in the books his initial plan was to travel with the Fellowship only as far as Rauros, and then leave those who headed for Mordor, and instead go to Gondor with Boromir, and I think it's reasonable to assume that said plan included him at some point presenting his claim to the throne. He was ready and determined and working towards it in subtler ways long before LOTR took place.

I feel like on a symbolical level you can see that in Narsil/Andúril, which is both a sign of his ancestry, and a symbol of his own claim to kingship. In the book he already carries it when we first meet him, but it is still broken; he keeps the sign of who he is on him, he recognizes and accepts his heritage and who he is is tied to his lineage, but he is not yet ready or willing to present his claim to Gondor's throne, the time for that is not yet come. It is still called Narsil or the sword that was was broken; it is a symbol of his ancestry, not of his own claim. But before he leaves Rivendell with the Fellowship, he has the sword reforged, and names it Andúril. The blade is whole again, because it is the time for him to go to Gondor and claim his throne. It is reforged at his request, and he names it, and so it is no longer symbol of only his lineage, but also of him personally and both his own capability and his own desire to be the king.

In the movie, not only is Narsil broken but it is initially kept on display in Rivendell. Aragorn knows of his ancestry, but he has not accepted it as part of who he is and is not yet willing to take on the responsibility that his heritage would place on him. Even as the Fellowship leaves Rivendell, the broken pieces are still left there. Whether or not Aragorn initially intends to go to Gondor (as I said I literally do not remember), he is not intending to present his claim for the throne, is not yet willing to do everything that fully accepting his heritage would require of him. It is only much later in the story, that Elrond, at Arwen's urging, has the sword reforged and presents it to Aragorn. In the movie it is also Elrond who tells Aragorn the sword's new name; Aragorn doesn't name it himself. Elrond thrusts the responsibility of kingship and of his heritage upon Aragorn, Elrond makes him claim it. And yes, Aragorn does accept it and embrace it, and turns out he is pretty good at it, but it is not fully his choice, it is other people and outside forces that convince him to take up the burden.

And as I implied before, the books also don't treat the Strider side and King Elessar side of Aragorn as mutually exclusive. He can be both and he is both, and they are not in conflict. He even chooses "Telcontar" the Quenyan translation of "Strider" to be the name of his house when he becomes the king of the Reunited Kingdom. It's also important to note that in the books, while he is not a king, he is already a leader; he is the chieftain of the Rangers of the North, and has been for a long time. He already knows the responsibility of a leader, and has already accepted it and acted according to it for a long time. Yes, it is a much smaller scale of things than that of being a king, but it is responsibility of leadership, responsibility over people, even so. Admittedly, the movies technically do not conflict with him being a leader already, but neither do they confirm it. The Grey Company is entirely cut out/replaced with the troop of elves from Lórien who appear at Helm's Deep and then are never mentioned again. The references to the Rangers of the North are few and far between, and it's never really in any way explained that they're also Dúnedain and descendants of the people of the kingdom of Arnor. And quite frankly there are parts of Aragorn's characterization in the movies that in my opinion simply do not make any sense if "ranger" means the same thing it does in the books and he is the chieftain of the Rangers, so I'm going to assume it's just not a thing in the movie canon.

Anyway, point was, in the book canon Aragorn does not need to reject one aspect of who he is in favor of another, but instead he is who he is, he knows who he is, and embraces both of those sides. I feel like that is also part of what makes him feel older and more experienced in the books, although part of that is also just the fact that he has more dialogue where he talks about things he has seen or experienced, gives exposition about lore stuff, and overall just shares his knowledge more, and there's more moments when you can see the way his past experiences have shaped him (whether that's moments where you can see the effects of traumatic experiences - there's been a post going on about that specifically recently, so I won't go into that - or memories of good times such as at Cerin Amroth in Lothlórien, or whatever). In a way the more humoristic side of him ties into that too, whether it be the intentional jokes and pranks, or the sarcasm and thinly veiled bitching when people annoy him, or the moments when he just gets unnecessarily dramatic about one thing or another in a comical way. All of that just comes together to make the character feel more complex, which again adds to the sense of age, like he's old enough to no longer feel the need to present himself in one specific way to others, but instead letting every side of himself show. It also just makes him feel more human in a way, because he's not just one thing and one thing alone.

Book!Aragorn does still face problems and conflicts, but his conflict is not about accepting or rejecting his heritage. Instead it is about meeting that responsibility, about taking responsibility for and protecting what he has claimed as his, about showing the people of Gondor not only the proof of his heritage, but also of his actual capability and competence to that job. This is a bit of a sidenote, but I've seen before on tumbr a post about how he actually takes his time before returning to Minas Tirith after Sauron's defeat, enough time for Faramir to heal, enough time for the city to start to recover or at least kinda find its balance and get things together. Enough time that the people of Gondor, if they'd wanted, could have decided that hey actually we've been doing fine with stewards for so long, what do we need a king for, we don't really want one. He didn't just barge back in when everything was still a mess and chaos and use that lack of balance to take control and establish his position, he took long enough that people would have had the time to consider it and actually decide that yes, we do want him to be our king. In the book his obstacle is not overcoming his self-doubt, it is proving himself to other people, to the people he hopes to rule (and, when it comes to the Rohirrim, the people he'll need to build a diplomatic relationship in the future, I guess).

In the movies, though, his main conflict is with himself, his main obstacle is his own self-doubt and whether or not he actually wants to be the king in the first place. This is also one of the things that makes him seem younger than the book version, because his main struggle is largely in deciding who he is and what he wants, he hasn't quite figured that out yet. I think he also ends up just kind of feeling a little less complex and a little more one-sided and more of an average hero (because let's face it, "am I worthy" is the typical fantasy hero's main dilemma and internal conflict) because of that.