We present a microscopic analysis of shape transitions of micelles of model linear nonionic surfactants. In particular, symmetric H4T4 and asymmetric H3T6 surfactants have been chosen for the study. In a previous work, it has been observed that symmetric surfactants have a strong tendency to prefer spherical micelles over a wide range of chemical potentials, while asymmetric surfactants undergo shape transitions between a spherical micelle at low concentration to other forms, mainly finite cylindrical micelles. This study combines the application of a two-dimensional single-chain mean-field theory (SCMFT) with Monte Carlo (MC) simulations of exactly the same systems. On the one hand, the characteristics of the SCMFT make this method suitable for free energy calculations, especially for small surfactants, due to the incorporation of relevant microscopic details in the model. On the other hand, MC simulations permit us to obtain a complete picture of the statistical mechanical problem, for the purpose of validation of the mean-field calculations. reveal that the spherical shape for the symmetric surfactant is stable over a large range of surfactant concentrations. However, the asymmetric surfactant undergoes a complex shape transition that we have followed by calculating the standard chemical potential as a function of the aggregation number. The results indicate that the system forms prolate spheroids prior to developing short capped cylinders that gradually grow in length, with some oscillations in the energy of formation. The most important result of our work is the evidence of a bifurcation where, together with the elongated objects, the system can develop oblate aggregates and finally a torus shape similar to a red blood cell.