No, they will not fight (atleast to the death, maybe just a friendly fight) But there is a difference between HashiMada and NaruSasu, relationship wise atleast (in a non gay way)
Sasuke is Virtuous, while Madara is not. Hashi has leadership qualities, while Naruto doesnt. Things between Naruto and Sasuke cannot be foretold.
In my opinion, Sasuke will either sacrifice himself for everyone's life, or Sasuke will become hokage, or be put into leadership positions.
Sasuke is more like Hashirama than Naruto. Hashirama was put into a leadership position, and so was Sasuke (of both Hebi and Taka) A lot of characters wanted Sasuke's power, much like a lot of characters wanted Hashi's power.
Sure, Sasuke is considered a traitor, but is he really. He left the village to get stronger to avenge his people. Then he wanted to attack the leaf because they were behind it all. Now he wants to be leader of the leaf so nothing like that happens again.
For Naruto, the only reason why he wants to be hokage is because it is a childhood dream of his. Also, he does not have the intelligence or the patience for it neither.