I'm several hours into FFXIII-2 now and my feelings are pretty consistent with most of the reviews that are out there. FFXIII-2 is an improvement over the first game in almost every respect. It seems Square-Enix just made a laundry list of the criticisms of the first game and tried their best to correct a majority of them.
Minor spoilers below:
I am one of those weird people that thought FFXIII was pretty good but I also thought it was one of the weaker entries into the series. As you can imagine, I am really enjoying FFXIII-2 due to the improvements. That said, Square-Enix didn't get everything right on the second try. The story can be a bit nonsensical at times and the dialogue suffers from it. However the voice acting is very well done. The actors that do Serah and Noel should be given major props for pulling off some corny lines extremely well. I think pretty much everyone will agree that Chocolina is a bit on the absurd side but you can easily skip her unimportant dialogue so she doesn't annoy me too much.
Essentially I am enjoying everything about the game except for its weak plot. I love the visuals, the battle system, and the admittedly eclectic music selections. Overall I'd give the game 4 out of 5 at this point. We'll see if I still feel the same way after I finish it.