Grand canonical Monte Carlo (GCMC) simulations assisted by histogram reweighting techniques were used to study the effect of chain flexibility on the solution phase behavior for cubic lattice short chains with 4-32 segments. This was done by varying gradually a stiffness parameter until the calculated mean end-to-end distance approached the fully extended length. For both flexible and stiff chains it was found that the critical temperature, obtained by mixed-field finite size analysis, increased with chain length and the critical density moved to lower values, in agreement with experimental observations. The extrapolated infinite chain length critical temperature was greater for stiffer chains. This was attributed to the larger number of favorable intermolecular contacts between longer and/or rigid polymer chains. Critical temperatures obtained in this work are in excellent agreement with previous computer simulations and theoretical predictions. It was also found that phase envelopes of flexible chains fell below and within the rigid counterparts. At high densities, long (r = 16 and r = 32) and rigid chains showed a tendency to form ordered dense structures which were not observed in fully flexible or short chains. By comparing values of the Flory x(1) and x(2) parameters, obtained from fits of the calculated phase diagrams at different degrees of chain stiffness, it was concluded that, when phase separation occurs, packing stiff rods leads to a smaller entropy change and a less endothermic process. The present results support the idea that, in polymeric systems, an increase in the stiffness of the chain backbone is equivalent to an increase in chain length.