Just Dance 3 and Dance Central 2 are different styles of dance game - and they have different music libraries. Here's a comparison of the two of them, if you're looking into getting a new dance game for your system.
I'll comment first that I have all versions of both games, so I'm familiar with the features on each. I actively enjoy dance games, so I'm their target audience for these types of activities.
The first thing to look at is the music library. If you hate the music a dance game offers then it really doesn't matter what the gameplay is like. You're just not going to enjoy it. The songs are similar, but certainly not identical. You could easily find that you adore 90% of the songs on one game and only 25% of the songs on the other. So that is step #1. If you are heavily swayed by the songs on one list, go with it. The game play will be similar enough to make that song list an overwhelming factor.
So let's say you look at the song lists and you enjoy both of them. You'd have equal fun with both songs. Now we get into the gameplay.
Just Dance 3 has "songs with themes". Every song has its own dancers and background. So when you sing a 60s song, you've got 60s themed dancers in a 60s themed area. You can only be those dancers. In comparison, with Dance Central you have a stock set of dancers, in a small list of locations. So every song you do, you choose from one of those locations and you choose from one of those dancers.
This is a preference call. If you adore one of the Dance Central dancers, and you adore one of the locations, you could be completely happy to dance every single song with that person and in that place. So if I adore a snazzy girl on the beach, I can dance all my songs there and be happy. On the other hand, I adore Just Dance 3's themes. I love doing Boogie Wonderland in a 70s disco with the fantastic outfits. I love doing Crazy Little Thing in a 50s drive-in with the greaser and his chick. So in my personal preferences, I like the Just Dance 3 side here. I do wish Just Dance 3 offered more choices within their theme though. They could have different skinned people in the Boogie Wonderland for example. It wouldn't be that hard.
Next, the moves. Just Dance 3 has real humans - "poster arted" - doing the dance. So it's a real live fluid human smiling and dancing with you. It's amazingly fun. Your moves are completely natural and feel like dancing. They did a lot of work making the moves be period authentic and match the style. So the moves in the 60s dance are 60s style moves, the moves in the 80s aerobics are aerobic moves and so on. I love that.
With Dance Central they are computer generated figures, and the moves feel and look much more artificial. Yes you're dancing in time with the music, but with a few exceptions they aren't what someone in an actual club would have done.
An example of this is "Venus" which is in both songs. The Venus moves in Just Dance 3 are similar to what someone in a club would have done. The Dance Central moves are more "gamey" - they're a bit dancy, but not as good.
Both games track calories / sweat points for those who want to use this as a workout tool, and Dance Central gets kudos in this area for having far better options to manage it. So if you're looking for a tool to help you lose weight, Dance Central gets the edge here.
Still, a lot of this comes down to fine details. In the end. I enjoy both games, and both are fun for different reasons. Really for me it comes down to the song selection. Go with the one you like the songs of. When I reach for a game to pop into a system, it's the songs I have in mind, not which one makes me wave left instead of right.
Post in the forums if you have any questions!