RapRadar has a great breakdown of what was actually said by both parties. But here was J Cole's quotes to MTV News about Drake calling himself Jay-Z and J Cole "Nas".
“You can’t call things like that, that early. You can’t say I’m Nas because, look, Nas was in the game for 16 years. What if I’m not here next year? What if you’re not here next year? I don’t think you can say stuff like that this early, but I understand what people are saying. At his status right now, he’s the most talked-about guy in the game. The Nas comparison is like, ‘He gets a little bit beyond the surface,’ but I feel like when it comes to those comparisons, it’s way to early. And you never know, 10 years from now, I could be Jay.”