Each of these kinds of energy has benefits and drawbacks.
Coal is good in the US largely because it is readily available. Using it relieves us from having to import fuel from foreign countries. It also creates jobs for the miners who extract the coal. Finally, it is relatively cheap. These benefits have to be weighed against the fact that it emits huge amounts of greenhouse gasses.
But nuclear has advantages over coal. The main advantage is that it does not emit greenhouse gasses. Like coal, it can help reduce our dependence on foreign oil. However, nuclear energy has two major drawbacks. It is possible for nuclear plants to have tremendously consequential disasters. It is also very difficult to find a place where spent nuclear fuel can be stored.
Overall, then, you have to be able to identify which of these characteristics is most important to you. If you think global warming is a huge issue, then nuclear is better. If you worry about the chances of disasters, coal is better.