Naruto - Yang, Sasuke - Yin (or reverse them)
The main reasons Naruto has been dumb as hell throughout much of the manga are plot driven. First, Sasuke is a genius who did train, but needed little training as everything came naturally to him, and even faster once he developed his Sharingan. Sasuke is Naruto's 'foil' thus Naruto is one to whom things won't come immediately to and he must work his ass off to obtain the power he seeks.
I also believe Kishi tends to use Naruto's naivete to explain how stuff works, such as senjutsu, shadow clones, and elemental affinity as a few examples. If Kakashi asked him if he understood about his wind affinity, and Naruto said, "Sure!" then we the reader would know nothing.
As well, I suppose Kishi felt there was a comedic relief.
Finally, he had no one to raise him as an orphan. In fact he was worse than an orphan because of the Kyuubi, such that no one wanted him around nor their children to be near him. Sarutobi basically only looked after him via Kakashi to make sure, I presume, the seal was OK and Naruto wasn't dead. Being born an Uzumaki at his time turned out to be a double-edged sword, and I have no idea where the Namikaze were. Jiraiya couldn't raise him given his destiny. Thus, unlike Sasuke who had Itachi and his father, Naruto had no one to teach him even the simplest things.
Now, Naruto has gotten pretty keen in battle. Fighting Nagato has changed him forever. He understands important concepts such as hatred/peace, forgiveness/vengeance, etc.
Why does he look so much smarter in battle than in real life? I think it's focus. In battle he's always highly focused. Now, he has something to focus on outside of battle such as ending the circle of hatred that is the shinobi system and trying to come up with peace, saving Sasuke, and even helping the Kyuubi. Thus, I expect him to be much smarter in both aspects of life, battle and regular.
However, no, he will never reach or surpass genius's like Shikamaru or Sasuke (not designed to). It's simply not in his character profile. However, I think his days of being dumb are mostly over, except for comedic relief.
Peace