At first glance, Neji is a cold and emotionally withdrawn ninja who is probably too arrogant for even his 'genius' reputation. On closer inspection this is...not completely incorrect. Despite appearances, however, his coldness is not due to a lack of concern or care for his comrades but an inability to express (sometimes a lack of understanding why he should try) those feelings for his comrades. While it may appear on the surface that he doesn't particularly care for the safety of well-being of those around him, he is fully willing to sacrifice his own well-being up to giving his life more than once for those very friends and teammates.
Due to his traumatic and difficult childhood, Neji has constructed such thick emotional walls and retreated so far behind them that even when he chooses to lower them for close loved ones he tends to still maintain what would be a certain cold distance on others. After his father's death and his subsequent blaming it on the main branch of his family (with good reason, considering their poor treatment of his branch up until that point) he became deeply embittered and cynical, becoming hateful toward both his own clan and those he felt were too naive or idiotic to understand the 'truth'. The latter, of course, was out of frustration and jealousy, due to his own seemingly hopeless struggle against 'fate', in effect raging against the naivety of his younger self.
His loss to the 'loser' Naruto and the revelation of the truth about his father's death helped to break the grip of hopeless cynicism on him, restoring some of his faith in freedom of choice, and helping to dispel the resentment and hatred he felt toward his clan as a result. In the aftermath of this, Neji began to make an effort to ease down the cold walls he'd built and reshape his view of the world, letting in his friends and clan as much as possible instead. Despite this, he finds it difficult to express his feelings toward his friends and clan, having spent such a large portion of his life without experiencing these feelings directed toward himself. To lesser degrees, he also struggles with expressing gratitude or praise at times, due to his unfamiliarity with such warm and friendly actions. Still, he makes an effort at expressing and correcting these behaviors regardless of the difficulty it poses.
Given the Hyuga's high profile nature, the clan is a very respected and dignified family. Neji tends to share this strong sense of dignity and unshakable seriousness, and this behavior can sometimes simply exasperate and highlight his apparent emotional distance. Further, this sense of propriety and dignity can cause him to appear humorless, as a poorly (or less than excellently) timed joke may be either ignored or immediately shut down by him. On the contrary, he does possess a sense of humor that those close to him will glimpse...but he usually prefers to reserve it for an 'appropriate' time and intensity.
On the other hand, while he often has no time for frivolity due to his pervasive sense of seriousness, it also means it is difficult to ruffle his feathers or antagonize him--although excessive ridiculousness is still something he has great difficulty putting up with, due to how very much it is the antithesis of his Hyuga pride and dignity.
Neji is dedicated and driven to his training and to his work, partly due to his Hyuga pride (it would be unacceptable to put forth anything but his full effort to such important things, especially when it would be a matter of missed potential should he fail to) and partly due to his (almost) lifelong drive to defy his fate as a branch member, and prove through his skill and talent that he is no lesser than any members of the main branch. This dedication extends to taking his duties, such as his missions, quite seriously and therefore brooking no argument against completion of nor mischief during those missions.
Much of Neji's life was composed of searching for a way to decide his own fate despite the strict rules against his family in the clan and the horrible jutsu placed upon him which could completely strip away his freedom and sense of self at any whim of the main branch. His father's choice to sacrifice himself against his uncle (a main branch member)'s wishes and Naruto's persistence in fighting a losing, impossible battle despite his status as the village's greatest 'loser' both inspired Neji in this search, as did the words of one of his exam proctors, who spoke of how even a caged bird would find a way to pry open the cage with its beak if given motivation.
It could easily be said that these three were the ones to inspire Neji's final act, throwing himself into the path of a deadly missile and choosing to die in the place of his cousin and the village 'loser' to defy both the main family's choice in his life and to defy those who would determine his life as 'better' or 'more important' due to his 'genius'. In the end, in choosing to die as he did, he finally reached and understood the freedom his father found in his own sacrifice. With his curse-mark gone and no one to make his choices for him he is, essentially, finally free and capable of pursuing his own fate, untainted by the control of others around him, from this point onward.