The importance of father figures. Kirk is aimless without the direction he receives from Pike. Similarly, Spock begins to attempt to reconcile the two halves of himself, and the relationship with his father, much earlier on, unfortunately due to a shared pain of the loss of Amanda.
Part of the theme of Star Trek is humanity reaching for its potential and Kirk isn't doing that, until Pike steps in. That's the difference between Kirk and nuKirk. One had a father figure and one didn't, and we see the development of both ("stack of books with legs" and "repeat offender").
Spock encounters a similar arc, and gets a direct mirror of how deep emotions run in Vulcans in Nero. We see that logic isn't just a difference between humans and Vulcans for the sake of story, but a means to control something that is quite dangerous. Nero's break with reality with the destruction of Romulus showcases this in his scene with Pike ("It has happened!") and actually reflects Spock's own reaction to Kirk's death.
Much of the character building in the films are used through mirrors of what the main characters could become. While there is the argument that knowledge of TOS might negatively impact viewing these films, I would argue that it is improved upon knowing what Kirk and Spock could be in Prime timeline informs the differences all the more, and I enjoy the films more-so because of it.