We report the formation of colloidal complexes resulting from the electrostatic co-assembly between anionic surfactants and cationic polyelectrolytes or block copolymers. Combining light and x-ray scattering experiments with cryogenic transmission and optical microscopy, we emphasize a feature rarely addressed in the formation of the electrostatic complexes, namely the role of the mixing concentration on the microstructure. At low mixing concentration, electrostatic complexes made from cationic-neutral copolymers and alkyl sulfate surfactants exhibit spherical core-shell microstructures. With increasing concentration, the complexes undergo a sphere-to-cylinder transition, yielding elongated aggregates with diameter 50 nm and length up to several hundreds of nanometers. From the comparison between homo- and diblock polymer phase behaviors, it is suggested that the unidimensional growth is driven by the ability of the surfactant to self-assemble into cylindrical micelles, and in particular when these surfactants are complexed with oppositely charged polymers.