Did Naruto even care about being strong before he met Sasuke? What has Sasuke been doing all his childhood?
See, comparing people is not that simple. You cannot compare the strength and mental of an healthy boy who is being tutored by brothers and parents with that of an orphan who does not even know what it means to be a human in society. Thus, you cannot compare Naruto and Sasuke before Naruto even start to really want to be a shinobi.
Madara was weaker than Hashirama because an uchiha without Sharingan is nothing, and because Ashura is stronger than Indra.
See, with Hashirama and Madara, we can do a comparison because both were raised by parents in the midst of an era of war. Hashirama's father was thinking exactly like Madara's father. Thus, in their time, children were already well trained shinobi to exploit all their potential. This explain why Hashirama could be stronger than a one tomoe Sharingan Madara.
I can guarantee that if Naruto were raised as shinobi by his parents in the same way Sasuke was raised as shinobi by his parent, Sasuke would last a single minute in a battle against Naruto when they were in academy. Just consider Naruto taking advantage of his uzumaki chakra pool, his father's intellignece and his mother's strength.
What I am saying is that Hashirama is not a special case. Rather, Naruto is a special case of a gifted child being outcast by the society, and lost because he has no parent. The answer to your question is that hashirama had parents who trained him to be a shinobi, and as Ashura's reincarnation, he was simply stronger than Madara.