First, a correction. The unit of energy is kilowatt hour (i.e. kilowatt multiplied by hour) not kilowatt/hour. Power, measured in kilowatts, is defined as energy per unit time, so to get energy units you must multiply by a time unit (such as hour), not divide by it.

The answer to this question is that it depends on the two specific plants you're comparing. Nuclear plants in the US are listed e.g. at http://www.eia.doe.gov/cneaf/nuclear/page/at_a_glance/states/statesal.html where you can follow the links in the table of states on the right to see the capacity of various nuclear plants. These run between 0.5 and 1.3 Terawatt (electric). The average capacity of US coal plants (calculated from a table in http://en.wikipedia.org/wiki/Coal_power_in_the_United_States ) is 1.245 Terawatt (electric), which is comparable.

Nationwide, in the US, coal plants provide about twice as much power as did nuclear plants, but this is because there are many more coal-fired plants than nuclear plants.

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Year-to-date, coal-fired plants contributed 44.4 percent of the Nation’s electric power. Nuclear plants contributed 20.2 percent, while 23.7 percent was generated at natural gas-fired plants.
- end quote - (from http://www.eia.doe.gov/cneaf/electricity/epm/epm_sum.html ).

As for the relative costs, while the fuel costs for nuclear generation are slight compared to fossil fuel generation such as coal, overall nuclear and coal generation costs are similar:

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Additionally and in contrast to oil and gas, nuclear fuel costs are low and relatively stable. Fuel costs now average less than one half cent per kilowatthour. This is well below the costs of major competing fossil fuels. Production costs for nuclear power, operation and maintenance plus fuel costs, are also low, averaging 1.8 cents per kilowatt-hour. This cost roughly matches coal and is significantly below the costs of operating a natural gas plant.
- end quote - (from http://www.eia.doe.gov/cneaf/nuclear/page/analysis/nuclearpower.html )