The play system on XIII-2 was infinitely better than on XIII.
They did away with the linear levels and allowed you to jump from any level to any other level, and even gave the ability to reset/restore levels to complete any side quests.
The crystarium was much simplified, and there was just one simple shop, rather than several different ones for each different item type. Weapon upgrades were dropped too and they resorted to simply buying the next one up at strategic locations.
They even harked back to VII a little with Serendipity which was reniscent of the Gold Saucer, and they also revived Chocobo Racing.
Sadly, the storytelling let XIII-2 down. I don't know if I was left wanting more at the end, but definitely felt like I deserved more!