The thing I learned, this year, is that there are more voicing possibilities with quartal chords. The thing I think, that makes a difference, is that the notes are spread apart, in 5ths (4ths depending how you look at it). This means that usually two of those notes will belong in the key, or go with the chord you're playing.
The way I add it, is to take the topmost note, of a chord that I'd normally play, and add notes (2 or more) a 4th below it.