They both play video, albeit the iPod classic has the advantage of more screen real estate.
iPod nanos have less space, but the iPod classic uses a hard drive, not solid state flash drives like nanos. Something to consider if you have butterfingers or want to use it for running/working out.
Price per GB, you can't beat a classic. If you have a huge library and want it Available to you at all times, the classic wins hands down. If portability and form factor are your main concerns then stick to the nano