Well, chances are, the Lovely Music iDs will initially be more expensive on eBay, since they would be in more demand (just like the +C and original iD). Also, I think I heard that the only differences between the two iD editions are the characters (Lovelin instead of Lovelytchi, as well as Melodytchi, on the LMiD), and the games included (I think a cooking game and a violin game are on the Lovely Music iD).
So, if any of the new characters and games interest you, and you're willing to pay a bit more or wait until prices go down, then you might want the Lovely Music iD. If you're a collector, then you could get one to further complete your collection. Otherwise, you might just be content with the regular iD.