DDR2 fixes some of the problems from the first version. First, it actually saves your settings (I personally got tired of having to turn off the hand markers every time I started up the game). Also, it allows you to start the groove arena over as a different user if multiple people want the challenge. And other seemingly broken aspects of DDR1 are also fixed -- the timing of arrows, difficulty level, etc actually WORK. I wish this had been the case in the original release. There's also more help for beginners, like bars to show the beat/arrow timing you can turn on, and the ability to slow down the song and arrows to take on a new challenge.
The songs - well, there's a mix of good and not so good. But I think that's to be expected. I got tired of dancing to the same songs over and over, so it's refreshing and welcome. It also seems like they're targeted towards easier play, with less difficulty on Difficult and Expert level. I haven't unlocked every song yet.
The graphics look better - both the dancers and stages. The Mii addition is kind of funny, but not that bad. You get a choice of certain Mii bodies to stick with your head, some better than others.
Basically this is what DDR1 should have been. If you've got DDR1 and felt shorted, I think you'll be glad to pick up DDR2. And if you're a beginner, I'd skip DDR1 and go straight to this version.