Brain-machine interfaces (BMIs) use signals recorded directly from the brain to control an external device, such as a computer cursor or a prosthetic limb. These control signals have been recorded from different levels of the brain, from field potentials at the scalp or cortical surface to single neuron action potentials. At present, the more invasive recordings have better signal quality, but also lower stability over time. Recently, subdural field potentials have been proposed as a stable, good quality source of control signals, with the potential for higher spatial and temporal bandwidth than EEG. Here we used finite element modeling in rats and humans and spatial spectral analysis in rats to compare the spatial resolution of signals recorded epidurally (outside the dura), with those recorded from subdural and scalp locations. Resolution of epidural and subdural signals was very similar in rats and somewhat less so in human models. Both were substantially better than signals recorded at the scalp. Resolution of epidural and subdural signals in humans was much more similar when the cerebrospinal fluid layer thickness was reduced. This suggests that the less invasive epidural recordings may yield signals of similar quality to subdural recordings, and hence may be more attractive as a source of control signals for BMIs.