A Nuclear Plant is a more expensive plant that generates $5p/m more than the Power Plant. It costs 75 more dollars (140$), and takes about 10 seconds longer to build.
This building is used for income generation. Like the Power Plant, it must be built near an Energy Crystal and a unit/building. It cannot be built if you already have a plant at the location you are trying to construct one.
It takes 9 minutes and 20 seconds for the Nuclear Plant to pay off its building cost on its own, and takes 15 minutes for a Nuclear Plant to start paying off relative to a power plant, as it has to cover much more building cost, when the Power Plant can pay for itself much quicker.
Once up for 15 minutes, both buildings will have generated a net increase of $85. From then on the Nuclear Plant will generate $5 more per minute.
Generally the plants built near the start of the game will be nuclear. Nuclear Plants should be built near your base or the bases of all your allies, or in a place you know they can be defended properly for an extended period of time.
It is generally a bad idea to go overboard with nuclear plants. They require a heavy initial payment, and will cripple your presence for the early game, leaving you susceptible to attacks. With the same amount of money at the start(300) you could buy two nuclear plants which will give you 45 p/m in total(10 by default) and 20 left over or get 4 power plants which will give you 55 p/m and 40 left over.