It's close for me. I have Public Enemy at 1A and Beastie Boys and 1B.
I think the Beastie Boys have had the better, more consistent career. Licensed to Ill was a game changer (even if you're not a huge fan, like me) and Paul's Boutique is as good an example of using samples in rap as we've ever seen. However, they lose just a few points because they can occasionally stray outside of rap.
Public Enemy may have been a shooting star, burning out after their incredible first 4 albums. But you can make a solid, legit argument that It Takes a Nation of Millions to Hold Us Back and Fear of a Black Planet are both top 5 rap albums of all time. The political vitriol is something no other artist in history, maybe with the exception of Bob Dylan, could communicate so well. It's a shame Flavor Flav has the reputation that he does today. While he was the court jester with his viking helmet, clocks and YEAAAAAHHH BOIIII!!!; he made it that Chuck D could deliver his social critique that set him apart from just about any rappers back then and today.
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