In this paper neutron diffraction properties of the dispersive double crystal (+n,-m) and (+n,+m) settings containing the bent perfect crystal Si(220) in symmetric diffraction geometry and the bent perfect crystal Si(311) in the fully asymmetric diffraction geometry with the output beam expansion are studied and compared. It has been found that the properties, namely, the width of the output double diffracted beam, of both settings strongly depends on the relative combination of curvatures of Si(311) crystal slab with respect to the curvature of the Si(220) one. Moreover, after the beam expansion the fully asymmetric diffraction geometry provides in both cases a highly collimated and highly monochromatic beam of a rather large cross-section of several square centimetres. Application possibilities, of such a beam, namely for neutron phase contrast radiography will be discussed.