The zombie and what it represents
Every memorable zombie fiction has a clear sense of what the zombie represents beyond itself: the loss of selfhood, the horror of consumption, the fear of infection, the return of the repressed, the collapse of the boundary between self and other. Writing zombies with metaphorical weight requires choosing a specific meaning and then making that meaning concrete in the story's specific choices. The zombie that represents the loss of a specific kind of community or relationship, and whose spread represents the spread of that loss, is doing more narrative work than the zombie that is simply a reanimated corpse. The specific mythology of your zombies (fast or slow, viral or supernatural, partial consciousness or none) should serve the metaphorical purpose rather than being chosen for genre familiarity alone.