I just tried the FFXIII-2 demo on my Xbox 360 and I'm completely in love. Square-Enix has done it again and is about to release another excellent game from the FF series. It looks amazing graphically, except for some very minor inconsistencies with the rain in the ruins where the demo takes place. But other than that the game has visuals on par with Uncharted 3 and other games with cutting-edge graphics.
The battle system works just like in XIII, for the most part. In the demo you only control Serah and Noel and the 3rd slot in the party is taken by a recruited monster, similar to what Namco did in Tales of Symphonia 2 for the Wii. Each monster has a "job" depending on what it does best, they can be commandos, ravagers, medics, etc and by switching the paradigms, you also switch which monster to use in battle.
You level up Noel and Serah using the crystarium in a way very much like FFXIII's but it's not exactly the same. While the monsters are leveled up using various items found almost everywhere, from treasure chests and shops to rewards after each battle. It also seems to be possible to focus on leveling up a few jobs instead of all of them to have the characters and monsters develop more depending on what each player prefers to do with them.
There are also some very cool QTE in the important battles where Noel and Serah do some very... impressive things to try and defeat the bosses, they reminded me of that Ninja Gaiden-ripoff called Ninja Blade that focused a lot on the QTE style, like God of War. But in XIII-2 you control the characters using the ATB system and the QTE parts only take a couple seconds before you take control of everything again. Oh, and they look really fucking cool. Like most Square-Enix cinematics.
The music seems... happier, like the transition from X to X-2 where the first one had a more serious and sad plot because of Yuna's purpose and the second had more cheerful music because everyone was happy and the quest in that game was more personal for her. XIII-2's music suffers from the same effect, but that's definitely not a bad thing and the songs in the demo are really cool. Fortunately, the Collector's Edition of the game comes with the entire soundtrack.
Overall, this is a day-1 purchase for me. I'm currently downloading the PS3 Demo to compare them as much as I can before making a decision and preorder the Collector's Edition on the console I finally decide on. I really recommend playing the first FFXIII before jumping on this one because the stories are extremely related. There are mentions to the events on the first game everywhere and if you didn't play it or understand it, you'll definitely have problems with the plot in XIII-2.