In the present work, we investigate the main differences in the lead neutron skin thickness, binding energy, surface energy, and density profiles obtained with two different density dependent hadron models. Our results are calculated within the Thomas-Fermi approximation with two different numerical prescriptions and compared with results obtained with a common parametrization of the nonlinear Walecka model. The neutron skin thickness is a reflex of the equation of state properties. Hence, a direct correlation is found between the neutron skin thickness and the slope of the symmetry energy. We show that within the present approximations, the asymmetry parameter for low momentum transfer polarized electron scattering is not sensitive to the model differences. DOI: 10.1103/PhysRevC.75.055805 PACS number(s): 21.65.+f, 24.10.Jv, 95.30.Tg, 26.60.+c 055805-2 DENSITY DEPENDENT HADRONIC MODELS AND THE . . . PHYSICAL REVIEW C 75, 055805 (2007)