Nicki Minaj is one of hip-hop’s old-fashioned superstars — an impressive technician, a character actor, a cross-genre fixture. Travis Scott is a star of the new generation, focused on aesthetics and reception more than his own technique.

For the last two weeks, Mr. Scott’s “Astroworld” has been the No. 1 album in the country, keeping Ms. Minaj’s “Queen” at bay. (On Twitter, she groaned over what she perceived to be the unfair circumstances helping boost the performance of Mr. Scott’s album.)

But while these two rappers seem opposed, they have commonalities: They both struggle with the album format, for one, and they are actively negotiating what their artistic identity should be.