I may be wrong, but I put the medians at a similar price. Both systems can go cheaper or more expensive. This is a little frustrating because 1 hour between major metro areas can cost 50-100x the 1 hour subway ride from the Bronx to Coney Island. In part this is because the train sets it's prices based on competition from airplanes.
MTA is heavily subsidized (it only covers ~50% of its expenses from its operational income), AmTrak is probably not.
Also, a train e.g. from NYC to Philadelphia looks inside much more like a plane (seats, tables, power sockets, wifi) than like a subway train, and obviously moves much faster. This all ought to cost more, even at zero profit point.
