Time
A non-stop flight from New York City to Los Angeles takes about six-and-a-half hours, or an additional three hours with one stop. The same trip by train, with one layover, will take about two-and-a-half days!
Cost
That same east-to-west coast excursion (and back) will run you about $400 by train, but about $150 less in the air. Your cost will skyrocket if you upgrade to a first-class flight or to a roomette or bedroom suite on the train, but your comfort level also will increase.
Safety
Statistically speaking, traveling by train and plane are two of the safest modes of transportation. Airports, however, have very strict passenger and luggage screening programs in place. Railroad stations are the exact opposite. The person who purchased the ticket(s) will have to show ID upon picking them up, but other traveling party members won't. And luggage isn't screened.
Comfort
Planes can be stuffy with limited leg room, and you may encounter sneezy, grumpy, snoring seatmates. While you're also subjected to a large group of people in an enclosed space on a train, aisles and seats are much wider.
Amenities
First class plane tickets will get you a bigger seat, more legroom and better menu options. A roomette on a train has a pull-down bed from the wall and a chair that converts to another bed, in addition to a small table. A bedroom unit will get you that as well as a private bathroom and shower.