In my opinion, Naruto and Sasuke are more "rivals" than anything else. The way Naruto (the show) is set up is that the more noticeable friendships come from the most intense, for lack of a better term, rivalry. Guy and Kakashi, Lee and Neji, Sakura and Ino. It's just the way it is in Naruto. I wouldn't necessarily call what Naruto and Sasuke have to be "the best friend connection." But, both know that the other has the potential to rival their own, so they deepened their bonds based on that, I believe. If one were to die/leave, who would the other compare their strength too? Those two are the strongest of their age group/generation, so without the other they would lose all determination to become stronger, and that unwillingness to become stronger and/or lack of a suitable counterpart to challenge them probably puts fear in the both of their minds.
Furthermore, I also think Sasuke called Naruto his best friend, since he knew Naruto was the one who could match him, and remember that Itachi told Sasuke that in order to unlock the three ringed version of his Sharingan, he had to kill his best friend. But Sasuke unlocked it even without killing him. As stated by Tobirama, the different levels of Sharingan are unlocked through their feelings, mostly pain. So, I'm pretty sure Sasuke felt more heartbreak in what he was doing to Naruto as Itachi did to him, and that's cutting off "family-tight bonds." However, I don't think Sasuke truly believed in his heart that Naruto was his best friend, just his eternal rival. Sasuke cut himself away from the world in order to prevent the pain he felt with his clans annihilation, so I'd be surprised if he considered anybody a true friend, to be honest. The only emotions he has left are towards Itachi, and coincidentally enough, those feelings, basically play a part in everything he has done so far and is going to do. To wrap things up, Sasuke probably spared Naruto for two reasons: 1) Sasuke considered his life after killing Itachi, and knew surpassing and staying ahead of Naruto would be his new life goal and 2) Sasuke wanted to reach his full potential without following in the footsteps of his brother.
To sum up, Naruto and Sasuke are more rivals than "best friends." The end.