Monte Carlo simulations are employed in order to analyze the structure of polyelectrolyte complexes consisting of two identical but oppositely charged macroions with varying chain stiffness. It is shown that two complex structures can arise depending on the stiffness of the constituent chains. Stiff chains are organized into a “ladder” structure in which chains are located parallel to each other and monomeric units are arranged into ionic pairs according to their position in the chain. Flexible chains form a globular “scrambled‐egg” structure with a disordered position of monomer units. The conformational transition between the two structures proceeds as a phase transition.