We present a comparative investigation of two opposite classes of self-assembled fibrillar networks. Ribbons and tubes having cross-sectional dimensions in the nanoscale can be formed in aqueous solutions of steroids derived, respectively, from deoxycholic (DC) and lithocholic (LC) acids. Rheological features distinguish energetic networks of DC ribbons rigidly fixed in cylindrical bundles and entropic transient networks of LC tubes weakly interacting in shear-sensitive suspensions. The two classes are characterized by their frequency sweep profiles, viscoelastic linear domains, scaling laws of the elastic shear modulus vs concentration, kinetics of formation of the networks, and their optical bireffingence aspects. A theoretical context for networks of rigid fibers IS used to account for the scaling exponents alpha in the G'(and sigma*) alpha C-0 laws (alpha=2.0 and 1.0, respectively, for DC and LC). The evolution observed in DC gets from ribbons to cylindrical fibers with monodisperse sections made up with four ribbons is an indication of an equilibrated balance between face-to-face attractions and untwisting elastic processes of the constitutive ribbons.