Vibrational energy transfer from the 61 level of S1(1B2u) benzene has been studied at low collision energies in supersonic free jet expansions for the collision partners H2, D2, N2, CH4, C2H2, and c-C3H6. Three of the four accessible vibrational relaxation channels in S1 benzene are found to be significantly populated: the 162 level, the spectrally unresolved 111 and 161 levels, and the 00 level. A small amount of transfer to the 41 level was observed with H2 as a collision partner. It is found that: (i) transfer to 00 is generally efficient; and (ii) the state-to-state branching ratios change substantially with collision partner. This is quite different from the trends observed for monatomic collision partners, for which transfer to 00 is absent and the state-to-state branching ratios are largely independent of the collision partner's identity [E. R. Waclawik and W. D. Lawrance, J. Chem. Phys. 102, 2780 (1995)]. It is further observed that the rotational contours of collisionally populated levels change. For a particular collision partner the extent of rotational excitation in the destination level increases with increasing vibrational energy gap. For a particular destination level there is considerable variation in rotational excitation amongst collision partners. The state-tostate propensity differences between monatomic partners and diatomics and small polyatomics are suggested to arise because angular momentum constraints are influencing the vibrational state-to-state branching ratios. 61→00 transfer is most affected: it is observed only when the collision partner can accept energy as rotational motion, and its branching ratio is particularly sensitive to the collision partner identity.