As a former Amtrak employee, all I can say is the sleeper rooms are very crowded, food is getting worse (check to see if the train you are going to be on has only microwave food or an actual diner with cooks), and trains are often late, at least on the west coast. Don't do it if you are in a hurry!
Some people really enjoy it; others don't. It is easier for children though as they can easily walk between cars and aren't as cramped as on a plane.
I can't say how things work on Amtrak now, but when my 30 year old nephew was only six we travelled Amtrak from Montreal to Washington DC and he had a marvelous time. It was an overnight trip, and customs between US and Canada was a hoot. The US customs agents asked if he had anything to declare, and he replied that he had new Jammies for the trip that he had recieved as a gift from his Canadian grandparents.
The club car had an electronic piano with a piano player that night, so I got him out of bed in his new jammies. The piano player asked him if he had any requests... He asked for the nutcracker and that is what the piano man played for him. That was one of those memories that will never go away
A good friend of mine did the Mt. one several years ago and into Canada on the train system there. They loved the Canadian part..but said the Amtrack really sucked!!! She had nothing good to say about it..just complaints.