Naruto, by far.
I never could get into the world of Avatar, it just doesn't appeal to me. DBZ was my childhood, but even I can recognize that its plot and themes are practically nonexistent. The entire plot could be summed up as some bad guy appears and then a protagonist unlocks a new form to beat him. That's about as deep as it gets. Further, the way power is distributed makes it so that battles can be analyzed by A > B > C logic... That can't be said for Naruto, or most other series.
I don't know much about Avatar because I just couldn't get into it. But, DBZ is entirely lacking in themes that Naruto played with (which were actually really numerous). Naruto's quality went into complete ****, especially after chapter 600 of the manga. But, it's narrative was stronger than DBZ's. Not even up for discussion. Sure, DBZ had a lot more influence over pop culture and anime/manga as a whole, but that's only because it's older. Naruto is much more inspired.
Also, Naruto has Itachi.
Kishi kinda ruined it.
