FFXIII-2 is just great in every way.
The characters are really well done. I like Serah as a protagonist because she's so normal and mature and smart and relatable. She doesn't need flashy powers or a complicated backstory. She's just a girl who wants her family back! The narration really helps you understand her goals and her thoughts. Noel is really interesting too. They put a lot of time into developing his thoughts on Snow and Caius, both of which reflect on his own character. (Because he seems parts of himself in both of them) I think Noel's character was really well done, in that way. Caius is also a great villain because his motivation is more personal and not just "I'm evil, so everyone should die!"
The plot is quite interesting too. The use of time travel is really fun. The quest to find Lightning is a good plot to get the story started, but it gets more interesting when you start to get into all the time travel stuff. You really have to forgive it for not making that much sense, and once you do that, it mostly makes sense. The ideas that are discussed in terms of Yeul and her fate are all very interesting and thought-provoking. And the journey of Hope and the others to help save the world is done quite well too.
Gameplay is a lot of fun. The battle system is just as good as it was in the original, though the random battles are a bit easy, I admit. Still, its no different than other RPGs where you can win by just mashing X...and I admit that's all you really have to do in FF13-2. Still, early on, the battles were okay. Then, I think, you get overleveled. I also don't really like the fact that the game basically uses random encounters. Still, the dungeon design is really nice. Lots of cool things here - The dark area in Yashas Massif, the rotating platforms in Academia, the rotating rooms in Augusta...I also love the little minigames they included. The crystal puzzles, the clock puzzles, etc, were all really fun. They really tried a lot of cool and inovative things with the dungeons, and I'm glad they did, even if I found some things to be a bit annoying. (Waiting 30 seconds at a time for rooms/platforms to rotate was a bit annoying...)
The game also has great voice acting, great music, and of course, great graphics. And more importantly, I just find it really fun. Even if the battles are simple, I love watching them play out, because the graphics are so nice that each battle looks like a choreographed cutscene. Plus, the battle system really is quite unique, and in the few fights where you actually have to do something, it is quite fun.