At my university's tech fair this fall there were promoters from Apple and Dell -- the Dell guy had a DJ and didn't know if it even worked (I managed to turn it on, didn't like it much though) and the Apple guy had an iPod mini hooked up to some Bose QuietComfort headphones. The iPod didn't take any great effort to turn on, wasn't as overloaded, et cetera.
The software's about the same on a DJ or iPod, but the iPod has a better hardware interface and the computer connectivity is better -- as has been stated, it's easier to use an iPod as a FireWire drive, it just shows up on your Explorer ('course, I don't use my iPod on my PC, but I assume it's as easy to do as it is to make it show up in Finder on a Mac, just a switch in iTunes). Moreover iTunes is compatible with the leading DRMed format (FairPlay AAC) and every major non-DRMed format (AAC, MP3, AIFF, WAV) save Ogg Vorbis, which isn't really that major. Also you can use Audible audiobooks (and political conventions/debates!) on an iPod, don't recall if you can on the Dell DJ.
Also if you ever get a Mac (need a small, cheap laptop that has a good battery? Or the best-value all-in-one, the only one with 64-bit?) the iPod will work just as well as it does on Windows, if not better yet (most iPod users seem to be on Windows so I imagine it works well). I think there are ways to make it work on Linux too, but on XP/2000 and OS X you can't beat the iPod.
The price difference isn't very big given what you're getting.