Large neutron star masses as the recently measured 1.97 \pm 0.04 M _ { \odot } for PSR J1614-2230 provide a valuable lower limit on the stiffness of the equation of state of dense , nuclear and quark matter . Complementary , the analysis of the elliptic flow in heavy ion collisions suggests an upper limit on the EoS stiffness . We illustrate how this dichotomy permits to constrain parameters of effective EoS models which otherwise could not be derived unambiguously from first principles .