I memorize tonal and atonal music basically the same way, except I can't rely on functional harmony and chord analysis the same way. But if something is sort of like a G major chord in first inversion, I remember it as "sort of a G major chord except there is a D flat HERE and an A sharp HERE" etc. Apart from that, I rely on aural, visual, tactile memory, as well as voice leading, melodic movement, intervals, if there is anything chromatic going on etc. It's still melodies and chords, just not fullowing the traditonal patterns.