Classic has lots more storage capacity in the same size package, better battery life, some new useful software features like selecting to jump to the first letter of an item in a huge list instead of having to endlessly scroll through the whole gigantic list of artists or song names, much better built in games, coverflow, supposedly more sturdy physically, and lots more little things here and there.
The only things you lose are very minor, including being able to output video to a tv using a non-proprietary cable, the ability to use it with a computer running OS 10.3 panther since the classic requires OS 10.4 tiger or 10.5 leopard, the ability to read long album or artist names in the now playing screen, a clock screen saver when you stay in the hold position that some people don't like, and a bunch of other very insignificant things
In other words, the classic has better battery life, much greater storage capacity, and then a whole bunch of small but significant improvements that add up to a whole lot.
EDIT: but if money is tight, the 5.5 is still a great and very capable machine.
