Yes, in the beginning I used to see him as much more like Sasuke. And even in his own team when he was a kid, Kakashi was the Sasuke figure. But he has transformed from the beginning of the manga and through the flashbacks of his team to be more like Naruto.
It's one of the reasons why he's my favorite character. Well that and lightning blade. But if you want to analyze it a little further. In Kakashi Gaiden, after Rin confesses her feelings to Kakashi, He has this line where he says, "I don't deserve you I'm scum."
It reminds of Naruto and Sai's conversation where he says that he doesn't deserve Sakura bc he couldn't fulfill his promise to her. That's why I don't really see Kakashi as an effective parallel of Sasuke bc if you really dig deeper you see they don't have that much in common.