The double perovskite Ba2FeMoO6 has been studied by neutron powder diffraction, Mossbauer spectrometry and x-ray absorption spectroscopy, and is compared with Sr2FeMoO6. It is shown that the size of the A-site cation has a large effect upon the nature of the low-temperature state, favouring the majority Fe2+/Mo6+ pair in the case of barium and the Fe3+/Mo5+ pair in the case of strontium. In both cases, an electronic transfer appears as T decreases, interpreted as the existence of a minority t(2g)down arrow narrow band, where the electron is itinerant.