It’s been debated to the point of irrelevancy. Most will tell you, Jay-Z over Nas, especially with the back-minded consideration that the former has Beyoncé on his arm. And Kelis probably hates Nas… So. Much. Right. Now!
It was always mostly about lyricism, amongst the variety of other factors that go into one’s musical experience. I still personally struggle with the debate. They are the two best rappers alive, and for my money, not alive, too (at risk of committing hip-hop blasphemy in not buying into the over-inflated value in the lives and skills of Tupac and Biggie after death).
If Jay-Z’s debut album, Reasonable Doubt, is a 9.8, then Nas’ debut, Illmatic, is a 9.9—I’m hesitant to give anything, even LeBron’s basketball skills, a perfect 10. Ask me in the early-to-mid-2000s (Blueprint albums to the Black Album), and I’d be more inclined to say Jay-Z. Ask me later in my timeline (Street’s Disciple/Hip Hop is Dead to Life is Good), and I’d be more inclined to say Nas (including up to this very day).
I’ll concede that some of Nas’ lows are lower than Jay-Z’s lows, and that Jay-Z’s overall career is more decorated. And I might also find some irony that Nas’ “Ether” effectively killed the mano a mano battle between the two (although Hova’s “Blueprint 2” retaliation off the Blueprint 2 album was pretty badass).