The difference is that a white person in a black neighbourhood will be put in danger by the criminal activity of private citizens. A black person in a white neighbourhood will be put in danger by an agent of the state who is purportedly responsible for dealing with criminality. The white person will have the backing of the state when seeking justice while the black person will be fighting the state.

In terms of the typical outcomes, in the first case those people are rightly considered criminals and will be held accountable if caught. In the second there is usually no accountability even though we know who carried out the action.