The main issue with transporting your car by train is availability. While there are train tracks covering most of the country rail companies do not offer auto transport service at every station. Basically the only year-round car shipping route is between Los Angeles and New York City. Amtrak also offers auto transport between Washington DC and Orlando but someone has to travel with the car. Sometimes routes will open up from Chicago but for the majority of people auto transport by rail is not a more appropriate solution than auto transport by truck. Advantages like lower price and safer transport are eclipsed by the sheer inconvenience.
With the amount of trucks on the road, rail can even be more expensive, even on the year-round route. Rail is being slowly phased out as trucks become more and more prevalent. It never hurts to explore your options, however.