The (j', Omega', epsilon') dependent differential collision cross sections of D2 with fully state selected (j = 12, Omega = 12, epsilon = -1) NO have been determined at a collision energy of about 550 cm(-1). The collisionally excited NO molecules are detected by (1+1') resonance enhanced multiphoton ionization combined using velocity-mapped ion-imaging. The results are compared to He-NO scattering results and tend to be more forward scattered for the same final rotational state. Both for collisions of the atomic He and the molecular D2 with NO, scattering into pairs of rotational states with the same value of n = j' - epsilon epsilon'2 yields the same angular dependence of the cross section. This "parity propensity rule" remains present both for spin-orbit conserving and spin-orbit changing transitions. The maxima in the differential cross sections-that reflect rotational rainbows-have been extracted from the D2-NO and the He-NO differential cross sections. These maxima are found to be distinct for odd and even parity pair number n. Rainbow positions of parity changing transitions (n is odd) occur at larger scattering angles than those of parity conserving transitions (n is even). Parity conserving transitions exhibit-from a classical point of view-a larger effective eccentricity of the shell. No rainbow doubling due to collisions onto either the N-end or the O-end was observed. From a classical point of view the presence of a double rainbow is expected. Rotational excitation of the D2 molecules has not been observed.