That "something" stretches back to the Afro-Caribbean layer of New Orleans culture. The music of both Dr. John and the Neville Brothers reveals itself, if you focus on it, as extraordinarily complex rhythmically. Hear everything that's going on, for example, in the rhythms of one of Dr. John's psychedelic swamp epics from his debut album, Gris-Gris, which after four decades still sounds like a set of discoveries other musicians have barely begun to exploit. Or hear the number of rhythmic forces pushing against the chorus in the Neville's famed "Hey Pocky Way," a song which goes back to their early years as the Meters. The rhythms in this music don't just make you tap your feet, they stretch your mind.
A way of music-making drawn on African sources allows these musicians to make almost anything their own. The Nevilles can cover a song like Leonard Cohen's "Bird on a Wire," not a likely choice for them, without breaking a sweat, while Dr. John applies his piano to pure jazz readings of pop standards. He has a way of tying together R&B, 1950s pop, jazz, psychedelia, and the straight-ahead rock of his one big hit, "Right Place, Wrong Time," and reattaching them all to their common root.
For the most part, these methods don't transfer well to the medium of recordings--they depend on making rhythmic decisions that evolve as part of the interaction between musicians and audience. That's one reason Dr. John and the Neville Brothers aren't as well known as they should be, and one more reason to warm up your late winter with New Orleans music at its best.