Phase separation in salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the mixtures are carried out and demonstrate that electrostatic interactions favor nematic ordering Coexistence curves for the symmetric mixtures are also constructed and are used to examine the effects of linear charge density and electrostatic interaction strength on rodlike polyelectrolyte complexation It is found that the counterions are uniformly distributed in the coexisting phases for low electrostatic interaction strengths dictated by the linear charge density of the polyelectrolytes and Bjerrum's length. However, the counterions also partition along with the rodlike polyelectrolytes with an increase in the electrostatic interaction strength. It is shown that the number density of the counterions is higher in the concentrated (or "coacervate") phase than in the dilute (or supernatant) phase In contrast to such rodlike mixtures, flexible polyelectrolyte mixtures can undergo only isotropic isotropic phase separation A comparison of the coexistence curves for weakly charged rodlike mixtures with those of analogous flexible polyelectrolyte mixtures reveals that the electrostatic driving force for the isotropic isotropic phase separation is stronger in the flexible mixtures.