Final Fantasy XIII was a disappointment, so my expectations for the sequel were low. However, Square Enix genuinely listened to the negative feedback from the previous game and did surprisingly well in creating a better product.
XIII-2 has opened up considerably in exploration. Instead of XIII's straight-forward, continuous corridor design; here you select destinations from a hub menu, and the game allows you to exit and explore other destinations anytime, at your own pace. Leveling-up is also fully open from the start, rather than restricting your progress throughout the story.
You can also collect enemy monsters and train them up to assist you in battle, though it's just really side-distraction for the most part. The soundtrack is really experimental for the series; a mish-mash or various genres that the series hadn't generally explored before. For the most part it works excellently, though some of the music might not be to your tastes.
XIII-2 falls flat in a few areas though. It has a terrible habit of recycling areas, of particular note, it reuses one certain location as 5 different levels, each with very few differences between them. The storytelling is messy and confusing, though the focus is more on the characters and their back-stories. What almost makes up for this is the villain; the strong, and surprisingly sympathetic Caius, who is absolutely one of the best antagonists the Final Fantasy series has seen in years.
All in all, the game is a significant improvement over Final Fantasy XIII, and due to the bargain prices it's going for these days, is definitely something to check out if you're a fan of the genre.