Naruto and Neji weren't bff's, but Naruto knew Neji enough to care for him and consider him a friend. So it's not forced that Naruto was sad to see Neji die. Also Naruto said he would keep everyone safe from Madara and Obito, and then they strike Neji down right in front of him, because Neji was trying to protect them. That was sure to bring emotion to Naruto.
Originally Posted by Joltik-Kid
As for why Hinata was less emotional. That was for three reasons. A) the real answer, so it could lead to the cover of volume 64's NaruHina moment. B) Shinobi aren't suppose to show emotion even if a teammate is killed in action. I think it was Sakura who stated the whole rule, back when this series was actually about ninjas. C) Hinata still holds a grudge against Neji for almost killing her. Okay I'm joking about the last one. But yeah, I think Naruto would get emotional for any of the Konoha 11 dying. Well maybe not poor Tenten. Have Naruto and Tenten ever spoken two words to each other in the manga? I know in the anime they've talked, but I can't recall in the manga. Someone let me know if they have.
RIP anime version of Glovehead. Pokemon Adventures will save you.