You don't take Amtrak because you want to get there fast, and you don't really take it because it's cheaper than flying. You take it because you can, and because it's more important to you to be (comparatively) comfortable instead of rushing from A to B. You take it because of the sights, the people, the chance encounters, the proximity to city centers that airplanes can never hope to match. It's an experience in and of itself that's distinctly foreign to many Americans, and one I wholeheartedly recommend.
Sitting in a roomette, crossing from Boston to LA over a long weekend, sharing delicious meals with total strangers as the countryside whizzed by (or we sat on a siding waiting on a freight train).
Just not comparable.