I loved XIII-2, every bit of it especially Caius. Such an amazing villain even if his motives are rather...poorly chosen. The battle system despite being the exact same as XIII's (minus the Feral Link) felt more polished, battles more fast paced despite being roughly the same length, and of course movies had better frame rates iirc. XIII-2 would be my favorite Final Fantasy if XII (12 for PS2) didn't exist).
Gameplay? Yes! It was 10x's better than XIII. I still miss having three regular people in my party, but the monsters weren't that bad.
Story? Kind of. It could've been better. I would've liked to learn more about the goddesses and Valhalla though. The time traveling was fun, but I didn't dig the open plot holes.
No. And Lightning's DLC story made it even worse in my opinion. Both endings were sad. I was one of the many fans that wanted a sequel where everyone had the "happily ever after", but that didn't happen. =/ Another favorite character was kicked off.