I don't have numbers to quote at you, but I would assume not. Fundamentally coal, nuclear, and gas-boiler (but not gas-turbine) power plants work the same way - you heat up water until it boils, and run the steam through a turbine to turn that heat into mechanical energy. I.e. the "cooling" is also the electricity generation mechanism. As a result same amount of heat should result in the basically same amount of electricity for each process, and since the water is being used in the same way they should be pretty much equal in water (use or consumption)/electricity output efficiency assuming they were built with the same era of technology...

Pretty much every power plant heats water to steam, then uses steam turbines to generate power. This is also how nuclear submarines and arcraft carriers work.

We never left the steampunk era.