We present microscopic calculations of light and medium mass nuclei and the equation of state of symmetric and asymmetric nuclear matter using different nucleon-nucleon interactions, including a new Argonne version that has the same spin-isospin structure as local chiral forces at next-to-next-to-leading order. The calculations are performed using auxiliary field diffusion Monte Carlo (AFDMC) combined with an improved variational wave function and sampling technique. The AFDMC method can now be used to successfully calculate the energies of very light to medium mass nuclei as well as the energy of isospin-asymmetric nuclear matter, demonstrating microscopically the quadratic dependence of the energy on the symmetry energy.