How much more efficient is nuclear power than coal power?

There could be different ways to address efficiency, but the most meaningful way would be the ratio of energy spent in order to produce the energy generated.
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Both coal fired plants and nuclear plants lose some heat in the generation process - not all of the heat generated converts into electrical power. Coal generates approximately 6.67 kW-h of electrical energy per kilogram¹, whereas uranium generates 360,000 kW-h of electrical energy per kilogram². That means it takes nearly 54,000 kG of coal to generate the same amount of energy as 1 kG of uranium. The good thing about using kG per kW-h is that ratio already factors in all the inefficiencies of the power generation itself, so the only thing left to consider is the energy spent to get the coal and uranium to the power plants.
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Mining requies energy itself, but so does transportation to the electrical generating site. It stands to reason that, since coal is transported in bulk, it is uses less energy to mine and transport than uranium. Let's assume that it costs 1000 times as much energy (not money, but actual energy) to mine and transfer 1 kG of uranium than it does 1 kG of coal. The energy efficiency of uranium would then be approximately 50 times better that that of coal.
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^{1 Source: http://en.wikipedia.org/wiki/Coal
2 Source: http://www.world-nuclear.org/info/inf02.html}