Black backgrounds have exactly the same limitation as white ones, i.e. they make the shot flat and 2 dimensional because they destroy the sense of distance between subject and background.
Unlike white (unless it's done well, which it very rarely is) black doesn't create flare, doesn't cause unwanted light to bounce all around the studio and doesn't damage fine edge detail. Black can sometimes create very striking results.
Grey (especially mid to dark grey) is perfect for producing gelled backgrounds (it can produce saturated colours, white can only produce pastel colours). Black can produce even deeper saturation but requires much more lighting power than most people have in home studios.
Grey can also be lit to produce a splash of light or colour if required, this creates a sense of depth.
Grey can be lit to produce white, but this needs quite a lot of lighting power. Left unlit, it can photgraph as black, but to do so it needs to be a fair distance behind the subject