In the late nineties I took a train from New Orleans to New York. The trip lasted over thirty hours. About five hours in I regretted the decision. I would have had a better experience if I had brought along more food and reading material.
I've never taken a train trip, but have looked into it. I found the cost quite high, fully as much as a plane ticket, and yet like Psiman's example, the travel time was really long. Also, I would have been sleeping in a chair, or more realistically sitting awake in a chair most of the time like I do on a 12 hour overnight flight to Europe. Of course, the train would be far longer than just 12 hours.
If the distance was shorter, driving would be the overwhelming best option. On the other hand, a sleeper cabin cost way more. Also, eating in the dining car would be very expensive, adding to the total cost of the trip. The train ride didn't compete at all as an option.
I think if I was rich, and could pay for a deluxe sleeper cabin and big, first-class style seat, and feel free to eat and drink in the dining car, then a long train ride could be very interesting, if the trip went through an area of beautiful scenery. That would be more like going for the cruise, where the travel experience is the point of the trip, more than the destination. If I just need to get to a destination, I don't think it can compete, ever with air travel being as miserable as it is.
Edit: I will add that if you have money, you can get the pass to skip the line for security, and you can fly first class. These take most of the hassle out of air travel.
Edit 2: I was just thinking that if I were on a 30 hour train ride, and slept in a bed, then I would wake up with bedhead, and would normally expect to take a shower. I expect I probably would be wetting my hair down in a 30" x 30" bathroom from an 8" diameter sink. It would be far worse for a really long trip like NYC to LA. You'd be going days without a shower.
