Energy cost contributes a large portion of the overall cost of desalinated water. Improving the energy efficiency of desalination plants is therefore a primary design goal. However, accurately evaluating and comparing the energy consumption of desalination plants that use different forms and grades of energy is difficult, especially for power-water coproduction systems in which primary energy consumption leads to both salable electricity and potable water. The power plant converts primary energy into grades of thermal energy and electricity usable by the desalination plant. To fully capture the thermodynamic and economic cost of energy, and to fairly compare desalination systems that use different grades of input energy, we must compare energy consumption not at the point where energy enters the desalination plant itself, but as primary energy consumption entering the power plant. This paper investigates a variety of metrics for comparing the energy and exergy consumption attributable to desalination in coproduction plants. Previous results have shown that reverse osmosis (RO) is approximately twice as efficient as multiple effect distillation (MED) on a primary energy basis. We then compare the primary energy consumption of MED and RO from a thermoeconomic perspective. The entropy generation at the RO membrane and in the MED effects are derived in similar terms, which enables a comparison of the overall heat transfer coefficient in an MED system to the permeability of an RO membrane. RO outperforms MED in energy efficiency because of a balance of material costs, transport coefficients, and cost of energy.