Different interface designs (the Classic uses that half split screen look for example).
Original 5th generation iPod came in 30GB, 60GB, and 80GB models. Classics come in 80 and 160GB models.
5th generation iPods can output video signal through the headphone jack and use generic A/V cables to hook up to TVs. Classic models only output to the dock connector and require specific Apple cables ($$$) to do this.
5th generation iPod can only play purchased Movies, but not rented movies. Classics can play both.
That is a quick list off the top of my head. I don't have a Classic, so I am not sure of other details that might exist (for example, 5th generation iPods do not support folders created in iTunes. Maybe Classic models do? I don't know).
Cheers,
Patrick