The relationship between linear momentum ($p$), kinetic energy ($K$), and mass ($m$) is given by the formula $p = \sqrt{2mK}$. Since the kinetic energies ($K$) of both bodies are equal, the momentum is directly proportional to the square root of the mass ($p \propto \sqrt{m}$). Therefore, the heavier body, which has a greater mass, will correspondingly have a greater momentum.