I hadn't actually played the original Crystal Chronicles before buying this game, as I don't own a gamecube - so in terms of how it compares to the first game, I can't comment.
However, in my opinion this is the best Final Fantasy game on the DS so far. The graphics are beautiful, even in-game, and the gameplay is fun and easy to understand and grasp. Despite it's length, I thoroughly enjoyed it.
Only two things let this game down - firstly, the voice acting, which was extremely grating after a while. There's only a certain amount of baby voices I can stand, and the first couple of cutscenes had me muting the sound a couple of seconds in. Secondly, the use of the touch screen. After playing Legend of Zelda: Phantom Hourglass and seeing the innovative ways it had you useing the touch screen, I couldn't help feeling that this game was a bit of a missed opportunity. Don't get me wrong, the gameplay was fun and much more engaging than FFIII, but it would've been greatly enhanced and a lot more fluid by using the stylus a little more.
Despite this, Ring of Fates is certainly worth a look.