The origin of the heavy elements in the Universe is not fully determined. Neutron star-black hole (NSBH) and {binary neutron star} (BNS) mergers may both produce heavy elements via rapid neutron-capture (r-process). We use the recent detection of gravitational waves from NSBHs, improved measurements of the neutron star equation-of-state, and the most modern numerical simulations of ejected material from binary collisions to measure the relative contribution of NSBHs and BNSs to the production of heavy elements. As the amount of r-process ejecta depends on the mass and spin distribution of the compact objects, as well as on the equation-of-state of the neutron stars, we consider various models for these quantities, informed by gravitational-wave and pulsar data. We find that in most scenarios, BNSs have produced more r-process elements than NSBHs over the past 2.5 billion years. If black holes have preferentially small spins, BNSs can produce at least twice of the amount of r-process elements than NSBHs. If black hole spins are small and there is a dearth of low mass () black holes within NSBH binaries, BNSs can account for the near totality of the r-process elements from binaries. For NSBH to produce large fraction of r-process elements, black holes in NSBHs must have small masses and large aligned spins, which is disfavored by current data.