We study the proton sideward and elliptic differential flow for Au+Au collisions at AGS energies (2 -- 8 A cdot GeV) in a microscopic relativistic transport model that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher hadronic excitations. In order to explore the sensitivity of the various differential flows to the nuclear equation of state (EoS) we use three different parameterizations of the scalar- and vector mean-fields, i.e. NL2 (soft), NL23 (medium) and NL3 (hard), with their momentum dependence fitted to the experimental Schrodinger equivalent potential (at normal nuclear matter density rho_0) up to kinetic energies of 1 GeV. We calculate the excitation function of sideward and elliptic flow within these parameter sets for Au+Au collisions and compare with the recent data from the E895 Collaboration as a function of rapidity, impact parameter and transverse momentum, respectively. We find that the best description of the differential data is provided by a rather 'stiff' EoS at 2 A cdot GeV (NL3) while at higher bombarding energies (4--8 A cdot GeV) a 'medium' EoS leads to the lowest chi^2 with respect to the data. However, the differences in the transverse and elliptic flows (from the different parameter sets) become of minor significance at 4--8 A cdot GeV. We attribute this insensitivity to a similar reduction of the vector potential in all models and to the dominance of string degrees of freedom at these bombarding energies.