What is the efficiency of nuclear power electric plants compared with coal-fired electric plants?

They're about the same: around 1/3, 33% to 35%, efficient, overall. That is to say, about 2/3 of the heat generated is passed to the environment as ... heat; and, on average, 1/3 is converted to electricity. Again, this is overall efficiency of the plants.

Too bad that utilities are not allowed to pump the heat from power plants into nearby homes for heating. It would not raise the efficient of the process but it would allow some direct human benefit from the heat. If this was done -- Nuclear power plants could be built in the heart of the city with steam lines flowing to homes. Free heat in WI, MN, ND, Montana, UP-MI VT would be a god send to these economies.

The process of heating water, making it steam, then running a turbine, converting mechanical energy into electrical energy , all these process is same in both nucs and thermal plants.

Since due to factor of safety nucs use lower temperature steam, the efficiency will be less in nucs!

Additionally , the nukes have another circulating cooling system for the reactor which the fossils don't have and this lowers the nuke's overall efficiency.