I would not call them annoyingly arrogant, both characters were oppressed and caused such acts.
Neji was from side branch family who was meant to be weaker and inferior also had a destiny which himself admitted he can't change. First, he was the living proof that one can surpass main family with, and he did it with his own efforts. Second, if he was way too arrogant he would not accept destiny was caging him. And he had his moments of compassion, care and sympathy.
Sasuke's clan was slaughtered and he was a loner. He had *****ing fangirls around that he had not been proud of. Also when he got beaten by Lee or overwhelmed by Orochimaru he accepted his defeat and moved along his way, also the fact that he wanted to challenge strong guys showed that he thinks he is not highest and mightiest among the bunch. About "Uchiha" pride; it was because he lost his clan and clinging to that part of his life and family to move further. His clan was viciously murdered and he was trying to avenge for them, that's the reason he got his pride.
They are not "annoyingly" arrogant, but were arrogant.
Annoyingly arrogant would would refer to Kiba and Sakura.
