The relationship between kinetic energy ($K$), momentum ($p$), and mass ($m$) is given by the formula $K = \frac{p^2}{2m}$. Since the momenta ($p$) of both bodies are equal, the kinetic energy is inversely proportional to the mass ($K \propto \frac{1}{m}$). Therefore, the lighter body, having a smaller mass, will have greater kinetic energy.